ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

This is a short history of the years when the idea of a union of all educators and researchers in the world, who work in graphics and graphics-related geometry, became a reality.

Starting with the organization of The 18th International Conference on Geometry and Graphics, which celebrates in 2018 its 40th Anniversary, as the Executive Chairman in office for the 2018 edition, I felt the need for a dedication, as well as for a certain visual identity for the Conference. These have been the two levers inspiring the design of the ICGG2018 Conference Logo, as represented in Fig. 1. Referring to the present digital character of Geometry and Graphics, a further input was that the Logo would be generated from a digital three-dimensional object. At the end, as the Logo tries to synthesize, I liked the idea of proposing a double dedication for the Conference: to Leonardo Da Vinci, after whom our Campus is named and to whom we would pay homage as a genius among the greatest showing the widest power of Geometry and Graphics in investigation and creativity between Science and Art, and to Giulio Natta, professor at the Politecnico di Milano and Nobel prizewinner for Chemistry in 1963—together with Karl Ziegler—, as a mentor of the profound function—and beauty!—of Geometry and Graphics in Science and Technology, even at the invisible scale of the molecular world. In addition, in order to further refer to the Conference Venue, in the official logo, presented as a view of the 3D model from a designated viewpoint located at the base level and looking upwards, the overall outline of the linear frame would allude to the letter “M”, first letter of the word Milan.

Although an increasing number of printed books around 1500 assessed geometry and arithmetic, specific evidence of their applications in the visual and technical arts is difficult to locate. Ten percent of incunabula addressed science, and were consulted by readers of books on music, as well as the artes techinae. Luca Pacioli’s Summa (1494) is an example of the developing mathematical discourse that taught argumentative reasoning and other practical and theoretical applications of mathematics in general. A century after Francesco di Giorgio’s 1478 ‘Opusculum de architectura,’ Ignatio Danti complained of the reduction of mathematical sciences among natural philosophers, such that “the little which remains to us is limited to some practical aspects learned from the mechanical artificers.” The development of mathematical studies chiefly among artist/engineers was rooted in the traditions of intellectual ‘omini pratici’ dating back to the treatises of Lorenzo Ghiberti, Leon Battista Alberti, Filarete, Piero della Francesca, and Francesco di Giorgio. Followers of this scholarship, generally around 1500 in the region from central Italy to southern Germany, believed that the universal form and function of Necessity required proportional estimation and numerical definition. Thus, approaches to problems in statics and dynamics often relied on arithmetic and Euclidian geometry, at a time when mathematical solutions were also sought for ancient Greek problems rational numbers could only estimate (e.g. doubling the cube, squaring the circle, trisecting the angle). I will use examples in the work of Leonardo da Vinci and his contemporaries as evidence of the central role of proportional geometry and arithmetic among artist/engineers for solutions in the natural sciences and practical arts.

In this introductory lecture I will try to summarize Natta’s contribution to chemistry and materials science. The research by his group, which earned him the Noble prize in 1963, provided unprecedented control over the synthesis of macromolecules with well-defined three-dimensional structures. I will emphasize how this structure is the key for the properties of these materials, or for that matter for any molecular object. More generally, I will put Natta’s research in a historical context, by discussing the pervasive importance of molecular geometry in chemistry, from the 19th century up to the present day. Advances in molecular graphics, alongside those in experimental and computational methods, are allowing chemists, materials scientists and biologists to appreciate the structure and properties of ever more complex materials.

This is a show-and-tell of what is essential exposure to geometry embedded in three examples, the quadric on three skew lines and stationary distances between conics and quadrics. With geometry one generalizes the specific. In other math for engineers general principles are introduced, i.e., theorems, etc., in the hope that given such rigorous stimulation the student will grasp all sorts of practical application. During this journey we will meet the familiar, e.g., linear algebra, and the not-so-familiar, e.g., line geometry and Gröbner basis solution of simultaneous polynomial equations.

Light and shadow are different in terms of physical characteristic and its phenomenon but originally, they are synonymous. It is because light is first perceived by having shadow, and the shadow does not exist without light. As a lighting designer, I have been practicing my work understanding this “designing light = designing shadow” since 40 years ago. By keep saying “designing shadow” without saying “designing light”, strangely, it leads very different outcome. Especially, we have a masterpiece by Junichiro Tanizaki called In Praise of Shadow describing Japanese aesthetic sense which is different from Western one, and as a result of this, my lighting design comes to be different from that in Western countries. I published one book called Designing with Shadow in 2010. In this book, I mention 13 keywords to describe shadow, and explain the lighting design. These 13 keywords include the words which might not directly relate research on geometry and graphics such as “Sparkling”, “Ambient”, “Layer”, “Coloring” and “Ecology”. So, I select 5 keywords from my work which might relate geometry and graphics, and would like to explore the ecology of shadow and its meaning as a design element. First of all, it is “Gradation”. This is the most important phenomenon of light and shadow for me which is the range laying between white and black. In other words, it is range that is neither light nor shadow, or the phenomenon that occurs where light and shadow intersect. I perceive the depth of shadow to the gradation that gradually vanishes. Other 4 words are “Contrast”, “Utsuroi”, “Sequence” and “Urban Planning”. In particular, “Utsuroi” is the Japanese unique word showing a relaxed time shifting. We cannot find a proper word to translate this in other languages. This is also magic of shadow that shows sift of time in nature, and this is a part of Japanese aesthetic sense.

Geometries in higher dimensional spaces have many applications. We shall give a compilation of a few well-known examples here. The fact that some higher dimensional geometries can be found within some lower dimensional geometries makes them even more interesting. At hand of some familiar examples, we shall see what these concepts in geometry can do for us. In the beginning, the meaning of dimension will be clarified and an agreement is reached about what is higher dimensional. A few words will be said about the relations and interplay between models of various geometries. To the concept of model spaces a major part of this contribution will be dedicated to. A full section is dedicated to the applications of higher dimensional geometries.

Visual illusion such as a double image sometimes is used as an experiment stimulus. A double image usually contains two alternative representations in one image. The observer could indicate what he/she sees from a double image under a specified condition such as specific presentation time or task. From the answers, researchers can investigate and further analyses to study human perceptual model. According to human contrast sensitivity function, we can compute a double image that allows multiple image interpretations to be modulated by the viewing distance. Such image is called a hybrid image. To produce a compelling hybrid image, the original hybrid image synthesis method could only use similar shapes of source images that were aligned in the edges. If any two different images can be hybrid, it would be beneficial as a new experimental tool. My recent research proposed the method of constructing a hybrid image that does not rely on the source images shape, an edge-alignment free hybrid image. In this talk, the hybrid image will be explored in detail from original method, the updated method, and its application. In addition to the hybrid image, this paper sums up several interesting computational visual illusions that can be applied in many areas from medical to education along with their underlying theory.

The purpose of this essay is to investigate on what process of vicarization the image makers (and with them philosophers, anthropologists, etc., and not only artists) subjected the traditional beholder, focusing their attention on those images that can be parastically generated by projective or natural mechanical processes. Particular attention will be given to those works that put their viewer into optical difficulties, subjecting them to retinal stress and relegating them to a situation of minus habens. This process, as we will see, will not only affect vision, but all the senses, delineating almost a pervading action of visual denigration that triggers a sinesthetic perception, with the odd purpose of accentuating the perceptual capabilities of the subject itself. An apparent contradiction, however, resolves itself in a revelation: it makes us blind, for we can see better what surrounds us.

This paper is a study of the spatial representations depicted in the films of the Japanese filmmaker Shinji Somai (1948–2001), who often used long takes. This study examines the characteristics of the long takes in his works. On the one hand, the spaces are rigorously constructed in order to integrate several elements into the scenes, but at the same time, spatial complexities and contradictions, which may be regarded as deconstructed spaces, are considered to appear. Moreover, the analogy between the spaces in films and architecture is discussed.

For the first time Cremona collected initial information and are the foundations of the classical theory of non-linear birational (Cremona) transformations of the plane and three-dimensional space [1]. Hudson in his monograph gave a more complete overview of the main issues of the classical theory of non-linear plane and three-dimensional space of birational transformations [2]. The main result of this paper is to develop the theoretical foundations of the construction of graphical models biquadratic plane transformations. The spatial mapping scheme of the two surfaces of the second order, established new patterns of producing four-four-correspondences between the two planes misalignment and theoretical principles modeling biquadratic canonical transformations of the plane. For graphical model and biquadratic transformation as well as for the study of their properties, biquadratic convert binary plane were mapped onto the plane of the two surfaces of the second order. At the same time dealt with three cases: (a) a combination of no ruled surfaces of the second order; (b) a combination of cylindrical and conical surfaces of the second order; (c) a combination of hyperboloid of second order [3]. Therefore, this article is dedicated to the development of the theory of building a graphical model transformation biquadratic plane misalignment between the planes and the development of the theory of biquadratic graphical model transformation plane and study their properties. Considered three cases: a combination of no ruled surfaces of the second order; combinations of conical and cylindrical surfaces of the second order; combination of hyperboloid of second order. Developed graphical models biquadratic twelve canonical transformations of the plane.

A simulation of the dynamic perception of the Necker cube in terms of a two-level quantum system, e.g. that of the hydrogen tunneling states of the ammonia molecules associated with the 24 GHz maser frequency, indicates that the neuro-physiological transformation leading, through a symmetry reduction, to perceptual reversal is controlled by the principles of quantum mechanics. An elementary neuro-physiological action similar to the Planck constant at a mesoscopic level is introduced.

The Geometry and Graphics have a fundamental role in the progress of the structural Engineering and buildings. The mission of modern representation for structural Engineering was basically dedicated to mastering the relationships between shape finding (and shape definition) and statics prediction (and statics calculation) (Ugo V in Fondamenti della rappresentazione architettonica, 1994) [1]. Build with ingenuity to simplify construction processes, dematerialize the masses to establish simple compositional rules, these principles on which the world of tensile structures is based, where ingenuity and form interpenetrate to produce results that challenge physics and science for a form at the limit of perfection. The geometry, at the centre of the design process from the concept phase to the construction is the control tool through which spatial intuition becomes a feasible project. The nature provides extraordinary examples of relationship between geometry, drawing and statics as like the spider’s web, a unique case of perfect interpenetration between harmonious design and advanced engineering. The analysis of the Geometry of Curves and Surfaces started from the first century after Christ with empirical experiments of the ancient Romans in the covers of theatres and arenas. The connections between ambient, nature and shape were studied in the “De Oratore” of Cicerone 55–54 B.C. and again from Vitruvio in De Architectura 15 B.C. The mission of modern representation for structural Engineering was basic basically dedicated to mastering the relationship between shape finding (and shape concept) and static ideas (and static studios) from the nature to the calculation. The aim of this paper is to discuss about the dialogue between this double geometrical approach and about its development over time. Proceeding over the centuries, first example of a roof tensile structure, which marks the start date of the tensile architecture, are the four-folds in steel, designed by the engineer V. G. Shukhov for the All-Russian Exhibition in Nijny-Novgorod, inspired by the architecture of nomad tents with the emblematic example of “Oval Pavilion”. The four pavilions for a few years remained the only example of tensile architecture, while succeeding fifty years, the projects mostly turned to experimentation of structures linked to International Exhibitions. It was in the following century, precisely in 1952, which took place the true beginning of the high season of tensile architecture, with the construction of the Dorton Arena, in Raleigh, USA. For the first time the concept of “tense surface, double curvature, pre-stressed” was introduced. A double curvature structure that presents itself with the form of a hyperbolic paraboloid. In this perspective is the natural world and its laws that must be investigated for the application to architectures, through the search for constructions that show natural processes with particular clarity the natural processes that create objects, with the search for the essential. Artificial mesh work like natural ones, the supporting function is guaranteed by the central curved “saddle” shape supported a series of rods. The natural model for pneumatic structures is instead traced to the minimal surfaces of soap bubbles. on this last the first study models of the structures are founded. Remarkable principles have been learned: from their working, to their possible aggregations and subdivisions. In this paper we want to emphasize at the duality between the kinematic graphics drawing (direct consequence of Cremona’s diagrams in the mid-19th century) and stress-strain shapes with predictions trough the 2D e 3D Finite Element Model (F.E.M.) analysis. Two cases of study are analysed the “Olympiastadion” in Monaco (Germany) by Otto Frei and the “Jesolo Magica”—Venice, Jesolo (Italy) one of the last design of Zaha Hadid.

In this work we deal with the problem: determine the locus of the point P such that the feet of the perpendiculars from P to (extended) sides of a given planar quadrilateral ABCD are concyclic. In general the locus is a cubic curve. We get a correspondence between some types of quadrilaterals and some classes of cubic curves. In the paper we answer several questions: For which quadrilaterals is the searched locus a cubic curve and for which a conic? What are properties of the cubic? For which quadrilaterals is the cubic decomposable? Which quadrilaterals correspond to singular cubic curves? What happens if a quadrilateral is tangential?

The large diffusion of BIM modeling within the study of historic buildings makes often necessary for researchers to integrate automatically models and graphic documentation (analogical and digital photographs, paintings, lithographs, etc.) derived from historical analysis. The study here presented study how to intersect three-dimensional digital models and analogical images using the basics of Projective Geometry. As already highlighted, within the process of virtual prefiguration of architecture, geometry has always acted as an indispensable scientific tool for the designer. It allows not only a correct and effective representation of structures and complex spatial configurations, but, above all, it inspires every creative design operation. In this way, the geometry reintroduces the ancient binomial between art and science. From an educational perspective, nowadays it is possible to proceed with a re-actualization of the projective processes, combined with the multiple attempts to “narrate” events on surfaces, (not only flat but also curves, narrations in which a person looks, for example, beyond the painted wall in a forerunner attempt that today we consider virtual reality). The study of Projective Geometry is central, making operative the well-established practice in the perspective, but in the opposite direction. In the digital space, it will be possible to project, from the point of view, the graphic information, existing on the image (representation plane), on the BIM objects. The advantage for the end user lies precisely in the projection by category of the information, which can therefore refer to the walls, some frescoes, the vaults, already modelled.

Here some results are presented from the ongoing research of the analysis of the drawings by Francesco Borromini, preserved at the Albertina in Vienna, relating to designs of cupolas, in order to highlight the geometric constructions and the proportional relationships in function of the realization of the projects. In fact, besides the symbolic geometries traceable especially in the most famous buildings, such as the San Carlo alle Quattro Fontane or Sant’Ivo alla Sapienza, evidenced even by Borromini himself, other and more decisive geometries are revealed by carefully observing the signed drawings. The research methodology adopted is based on comparing what emerged from the analysis of the drawings, the study of the treatises concerning the construction methods of the cupolas and the results obtained from the survey by means of a 3D laser scanner. The survey, in fact, becomes the tool to ascertain the correspondence between the theoretical form underlying the drawings, and the realized form, including the provisional works that determine the geometric conformation, verifying the link between the geometric-graphic reasoning related to the load distribution and the consequent dimension of the components.

The use of topological transformations in solving the problems of descriptive geometry is that these transformations carry out the non-uniform deformation of space, enabling one to map the non-closed curve on the line and the closed curve on the circumference. The problem is solved with the participation of projections of deformed figures, and then the result is returned to the original projection. For practical use of topical transformations, it is necessary to establish the graphically represented compatibility for each corresponding point of the transformed and initial spaces. The following positional problems are solved in the paper: (1) Any frontal contour surface having same or similarly located elliptical intersections and the triangular prism are represented. Construct their intercepting line; (2) Any frontal contour surface having identical or similarly located elliptical intersections and the horizontally projected plane are represented. Construct their intercepting line; (3) The elliptic paraboloid and frontally projected cylinder are represented. Construct their intercepting line. The results of the paper can be used to solve technical and constructive problems.

We describe an algorithm that creates a fractal pattern within a planar region R by ranplacing within it progressively smaller copies of a subpattern or fill-shape. After placing i copies of the fill-shape, we use the term gasket to describe the unfilled part of R. The size of the next fill-shape is determined by a constant $$\gamma $$ times the remaining area of the gasket divided by the total perimeter of the gasket. Experimental evidence is presented indicating that the areas of the fill-shapes obey an inverse power law for large i.

The caustic curve as a “burning curve” corresponds to its name only for a planar problem (2D). This is observed in flat sections of the congruence of reflected and refracted rays, when the normals to the surface lie in the cutting plane. For the congruence of reflected rays, i.e. for the 3D problem, the zone of maximum concentration is the quasifocal line. The surface of the caustic is the focal surface of the reflected ray congruence, but is not a zone of maximum concentration. To investigate the reflecting properties of surfaces of revolution, the congruence of reflected rays is stratified into a one-parameter set of reflected surfaces. It is proved that the quasifocal line remains an invariant of the reflecting surface for any stratification of the reflected ray congruence. The search of a zone of the greatest concentration of the rays, reflected by the surface has practical interest and can be used in designing solar installations for converting solar energy into thermal or electrical energy, in construction of reflecting surface of lamps and also in the designing the interior and exterior of buildings. That is why the quasifocal line theory will be proposed.

The extraction of feature lines on surfaces approximated by dense polygon meshes provides an effective one dimensional visual cue for the understanding of 3D shapes. Detection of directions over meshes is a crucial prerequisite for the extraction of such feature lines as it determines where and how the lines should be generated on meshes. While the majority of the feature lines proposed so far are defined based on classical definition of curvature in a discrete differential geometry context, extraction of curvature information from an integral invariant viewpoint has been proposed comparatively recently. This paper provides a systematic discussion over various critical directions including but not limited to principal directions of curvature, based on integral invariants defined over local neighborhoods on meshes. We categorize the critical directions with our framework, address their implementation, and present the result of implementation and observation from the viewpoints of effectiveness, robustness and computational costs.

We try a generalization of the theorem of the angle of circumference to a version in three-dimensional Euclidean space and ask for pairs $$({\varepsilon },{\varphi })$$ of planes passing through two (different skew) straight lines $$e\ni {\varepsilon }$$ and $$f\ni {\varphi }$$ such that the angle $$\alpha $$ enclosed by $${\varepsilon }$$ and $${\varphi }$$ is constant. It turns out that the set of all such intersection lines is a quartic ruled surface $$\varPhi $$ with $$e\cup f$$ being its double curve. We shall study the surface $$\varPhi $$ and its properties together with certain special appearances showing up for special values of some shape parameters such as the slope of e and f (with respect to a fixed plane) or the angle $$\alpha $$.

In the paper we study equidistant sets (midsets) of a conic and a line. We show that it is a part of a curve of order 8 if the conic is an ellipse or a hyperbola, and it is a part of a curve of order 6 in the case of parabola. We study the properties of the obtained curves such as their behavior at infinity and the existence of singular points.

The isotomic conjugate of an arbitrary point P with respect to a given triangle $$\triangle ABC$$ is the intersection point $$P^{'}$$ of the isotomic lines relative to the cevians through the point P. Furthermore, the isotomic transformation of a geometric object is defined by finding isotomic conjugates with respect to a triangle $$\triangle ABC$$ of all points on the geometric object. The isotomic transformation is a quadratic transformation for which various properties are known. In this article the isotomic transformation will be applied to a given fixed point P with respect to a one-parameter family of triangles $$\triangle ABC_i$$, such that two vertices $$A,\ B$$ are fixed and the third vertex $$C_i$$ lies on a geometric object. It will be shown that this new transformation is a cubic transformation and some properties will be stated.

We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over Hamiltonian quaternions only have two. Split quaternion polynomials of degree two are related to the coupler motion of “four-bar linkages” with equal opposite sides in universal hyperbolic geometry. A factorization corresponds to a leg of the four-bar linkage and during the motion the legs intersect in points of a conic whose focal points are the fixed revolute joints. The number of factorizations is related by the number of real focal points which can, indeed, be six in universal hyperbolic geometry.

We consider a problem of constructing algebraic surfaces on the basis of Grassmann’s ideas. We consider the surfaces of the second and higher orders with the purpose of obtaining their Grassmann’s extensive equations and their images in Java environment. The works (Banai and Manevich in Proceedings of the 6th International Conference on Engineering Computer Graphics and Descriptive Geometry, Tokyo, Japan, 1994; Manevich and Sluzkin in Linear Constructions of Grassmann, Kwant, 9 (in Russian). Moscow, pp. 19–22, 1977) [

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] were devoted to construction of flat curves of high order on the basis of Grassmann’s ideas. It should be noted that in the catalog of mathematical models of surfaces (Schilling in Catalog Mathematischer Modelle Mit 106 Abbildungen. Siebente Auflage. Leipzig 1911) [

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], and in Pabler and Lordick (J Geom Graph 21:263–271, 2017), Velichova (J Geom Graph 19:13–29, 2015) [

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,

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] one can see the physical models and the computer images of high degree surfaces. For the construction of the algebraic surfaces of high degrees according to Grassmann points, planes and lines are given as a geometric basis. Linear operations such as the joining of two points by a straight line and the construction of intersection point of straight line with a plane are conducted sequentially. The last operation in this sequence—the intersection of a straight line with a plane generally gives the point of the desired surface. It is shown that on certain straight lines in the process of constructing a surface, projective rows of points are formed. The surface equation is seen from the record of Grassmann extensive equations. The proof that the resulting set of points in space belongs to a high degree surfaces for a number of cases is given by the method of projective geometry. Most of the constructions are based on the G. Grassmann statement:

Let there be a certain number of fixed points, straight lines and planes in space. An arbitrary point X is associated with these elements by means of connections and intersections. If as a result of such constructions it turns out that certain four points lie in the same plane or certain two straight lines are intersected, then the point X belongs to an algebraic surface whose order is equal to the number indicating how many times the point X participated in the constructions. (Klein in Linear Constructions of Grassmann, pp. 220–224) [

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On the basis of this theorem we write a computation algorithm for finding images of surfaces of high degrees. It should be emphasized that all the extensive equations remain invariant when the coordinate system is replaced. Usage of the proposed constructions makes it possible to understand more deeply the various methods for the formation of algebraic surfaces, which can be useful in the study of various sections of analytic and projective geometry.

In this paper we study a family of compact 3-dimensional manifolds, i.e. space forms - more popularly, finite worlds - that are derived from famous Euclidean and non-Euclidean polyhedral tilings by the unified method of face identification, i.e. logical gluings. All these seem to have application in modern crystallography, as fullerenes and nanotubes!?!.

For lightweight structures in the field of architecture and civil engineering, concrete shells with negative Gaussian curvature are frequently used. One class of such surfaces are the skew ruled surfaces. To model such surfaces for the purpose of form-finding, we use the line geometry model of the Study sphere in the space of dual vectors. It allows the mapping of lines of the three-dimensional Euclidean space into points of the four-dimensional model space. The correspondence of minimal ruled surfaces, which are the helicoids, with geodesics on the dual unit sphere can be handled with the dual Rodrigues formula. This paper presents a proof of the formula and extends it to a general form, which avoids exceptions like parallel rulings. This approach also speeds up the interpolation algorithms for form-finding. The line geometry model, as implemented in Rhinoceros3D’s plug-in Grasshopper, was used to design a small thin-walled footbridge of concrete in cooperation with the TU Berlin. The formwork was prepared with a hot-wire foam cutter at the TU Dresden.

The locus $$k_\alpha $$ of all points where two different tangents of a planar curve k meet at a constant angle $$\alpha $$ is called the isoptic curve of k. We shall look for curves k that coincide with their isoptic curves $$k_\alpha $$ and call them autoisoptic curves. Describing a planar curve k by its support function d allows us to derive a system of two linear ordinary delay differential equations that have to be fulfilled by d in order to make k an autoisoptic curve. Examples of autoisoptic curves different from the only known examples, namely logarithmic spirals, shall be given. We do not provide the most general autoisoptic curves, since these involve ordinary delay differential equations with time dependent delays. We only treat the case of constant delays.

In this paper we investigate some properties related to the Brocard circle of a given triangle ∆ABC. Four of them correspond to the special point of a triangle that satisfies some conditions. Another one corresponds to the special case of ∆ABC for which the relation $$ ({\text{AC}}^{2} + {\text{AB}}^{2} )/2 = {\text{BC}}^{2} $$ holds. We analyzed the case where a symmedian is a tangent to the Brocard circle. We found some interesting properties related to the Brocard circle for right angle triangle and for isosceles triangle.

In this paper we analyse ruled surfaces in Lorentz-Minkowski space in terms of their structure functions. We are especially interested in ruled surfaces which do not have a Euclidean counterpart, that is, surfaces with null rulings, and in particular, so-called B-scrolls. For ruled surfaces in Lorentz-Minkowski space, we establish relations between their structure functions and curvatures. Structure functions can be used for e.g. proving the classical Dini-Beltrami theorem which states (in Euclidean space) that a ruled skew Weingarten surface is a piece of a helicoidal surface. In Lorentz-Minkowski space, the problem is more complex, due to the different types of surfaces with respect to their inherited metrics. It turns out that all null-ruled surfaces are Weingarten, however their structure functions need not be constant. In this paper we analyse helicoidal surfaces among Weingarten null-ruled surfaces in terms of their structure functions.

On a sheet of paper we consider a curve $$\mathbf{c}^*(s)$$. ‘Curved paper folding’ (or ‘curved Origami’) along $$\mathbf{c}^*(s)$$ folded from the planar sheet yields a (spatial) curve $$\mathbf{c}(s)$$ while the paper on both sides of $$\mathbf{c}(s)$$ turns into two developable strips $$\varPhi _{1,2}$$ through that curve. We examine the very special case of a configuration where the two surfaces $$\varPhi _ {1,2}$$ happen to be cones with different vertices $$\mathbf{v}_{1,2}$$. Such a triple $$(\mathbf{c}(s), \mathbf{v}_{1}, \mathbf{v}_{2})$$ shall be termed ‘triple for curved folding with pairs of cones’. In this paper we prove the following characterization of such triples: $$(\mathbf{c}(s), \mathbf{v}_{1}, \mathbf{v}_{2})$$, in general, is a triple for curved folding with cones iff the developable surface enveloped by the osculating planes of $$\mathbf{c}(s)$$ is tangent to some quadric of revolution $$\varPsi $$ with two different real focal points on its axis of rotation. These real focal points of $$\varPsi $$ are the vertices $$\mathbf{v}_{1,2}$$ of the two cones. If the curve $$\mathbf{c}(s)$$ happens to be planar we arrive at one of the following special cases: The two vertices $$\mathbf{v}_{1,2}$$ have to be symmetric with respect to the plane of $$\mathbf{c}(s)$$, or both, $$\mathbf{v}_{1}$$ and $$\mathbf{v}_{2}$$, are contained in the plane of $$\mathbf{c}(s)$$.

The subject of this research was Kasuga Gongen Genki, an emaki consisting of 20 scrolls with text and images depicting tales of the miracles performed by Kasuganokami, the deity enshrined at Kasugataisha. The subject of this research was a religious emaki, so unlike narrative emaki the story does not focus on the same characters. There are different characters in each section, and several of the same buildings are repeatedly shown in the backgrounds. There are pieces of text with year numbers specifically related to the narrative, telling the viewer when the story occurred. Buildings depicted through oblique projections can create a pictorial space that has multiple viewpoints, as in the case of perspective projection. The depicted scene may appear as a photograph that can capture a moment in time, but unlike in a photograph, the building can be observed from multiple viewpoints. This could make the viewer experience a longer time span, rather than looking at merely a fleeting moment captured in time. I concluded that the typical depictions of Kasugataisha, despite the passage of time, indicate that repeated miracles took place in the same location, as if to emphasize that the divine protection of the Kasuga deity is eternal and omnipresent. In the past, Japanese people were devoted to Kasugataisha, and today the location hosts visitors from many diverse cultures.

Inspired by recent publications of K. Myrianthis and of A.W. Akopyan and A.I. Bobenko, two different arrangements of circles on the sphere are studied. The first one originates from Phyllotaxis, a topic in plant morphogenesis, and gives rise to a polyhedron with hexagonal faces and a covering of the sphere with circles in a spiral arrangement. The second is related to a Poncelet grid on the sphere. The extended n sides of a closed spherical billiard within a conic form a net with a finite number of quadrilaterals with incircles. Orthogonality transforms it into a configuration of n concurrent lines where each pair is ‘concircular’ with $$n-2$$ other pairs, i.e., the four lines are inscribed into a cone of revolution.

Mobile architecture is the one of the main themes of architectural history of 20th century. These examines were explored by Jean Prouve, Buck Minster Fuller etc. The objectives of this research intend to examine the potential feature of so-called Mobile Space focusing on the double deck model that has a system of folding structure. To figure out the distinctive feature, a prototype was made to practice the utility of double deck mobile space. The prototype is able to transform into double deck when it sets up to the ground, and fold into single deck when it’s pulled by wrecker. Researching about the precedents of expanding-mobile-spaces, most examples were using horizontal extension system. This research examines exploring the way of expand the space in vertical direction with using folding structure. This system will mostly contribute land efficiency. In the prototype making process, a ground deck space was constructed using two-by-four method structure with 100 mm-glass-wool insulation between the panels. 40 mm by 40 mm steel frame was used as the folding structure of upper deck and enveloped by white membrane. Next phase, this prototype moved into practical use to find out some issues. Regarding those issues, folding system should be refined so to minimize down the setting up time. And structure frame of upper deck and the panels should reduce weight so to refine workability. Then the use of this double deck structure will be explored.

The graphical approaches associated with the philosophy of mind and logic have been underused so far in the visual literacy. This paper aims to extend the graphical methods of logical analysis, by constructing a multi-dimensional geometric model, using differential geometry concepts. The model features two qualitatively different representations of logical space, based on Wittgenstein’s Tractatus, where one is graphed on the Cartesian and the other on the polar coordinate system. Each representation comes with its own spatio-temporal structure of contained modalities, that Wittgenstein calls propositions. These propositions, geometrically translated as variables, form every line of reasoning in space, and provide pictures of the case reality. According to Wittgenstein, every form of reality is composed of space, time and color (meaning) and only through this configuration its picture is complete. In the geometrical model, for every point in space, the temporal character is specified by its positional declination, and the potential variability of its meaning is depicted with a color map. For example, if white and black represent a certain “p” or “~p” attribute, then a proposition’s light or dark tonality specify its logical tendency. This mathematically underpinned composition of entities forms a complete geometrical structure with analogically measurable units that can shed some light on forms of causality between the mental phenomena. The structure operates as a function and provides a graphical representation of logic in terms of space. Consequently, the model’s ability to graphically plot logical interrelations may introduce a new methodology of modeling phenomena and processes which can be applied in theoretical studies and combined with the natural sciences. As an instrument of direct assessment and suggestion, it can strongly contribute to logical analysis. This is notably important in regard to the modern-day philosophy of mind, which has a tendency towards fragmentariness as it separates the metaphysical qualities from the scientific knowledge.

Paper brings classification of manifolds determined as Minkowski mixed triple combinations of three different curve segments represented parametrically by their vector maps. Some intrinsic differential properties of resulting manifolds are derived, namely those based on the properties of original curve segments chosen as operands in the respective Minkowski point set operations. Minkowski mixed triple combination can be determined in more different forms considering equal or not equal parameterization of the three basic curve segments, while resulting manifolds are found to be of dimension 1 to 3 consequently. Parameters of these combinations are powerful shaping tools influencing considerably geometric and aesthetic characteristics of the resulting objects. Various forms of manifolds determined by means of this generating principle are presented, including examples of manifolds determined as various Minkowski triple combinations of three circles positioned into different planes in the Euclidean space, and existence of their singular points is discussed.

Pentagonal quasigroups are IM-quasigroups in which the additional identity of pentagonality holds. Motivated by the example C(q), where q is a solution of the equation $$q^4-3q^3+4q^2-2q+1=0$$, some basic geometric concepts are defined in a general pentagonal quasigroup. Such concepts are parallelogram, midpoint of a segment, regular pentagon and regular decagon with their centres. The connection between pentagonal and, much better known, GS-quasigroups is mentioned. That connection enables introduction of more geometric concepts in pentagonal quasigroups. In this article some theorems of the Euclidean geometry which use all these concepts are stated and proved in pentagonal quasigroups.

A special 3-dimensional model of more-dimensional cubes is described in the paper. The parts of this are 3D models of the lower-dimensional elements of the cube. These have rhombic faces that are congruent with the faces of the model of the whole cube. The suitable combinations of all these elements touching each other by the congruent faces create periodical space-filling tessellations. The spatial mosaics gained this way can have helical and fractal or fractal like structures after different reconstructions. The planar intersections of the spatial tessellations provide series of plane-tiling patterns that can be also restructured in order to have more sophisticated mosaics. The topic can have relations to industry, arts and design. Some new constructions are described and showed by figures in the paper and animations of the gained patterns are viewable on a referred home page.

Starting with a cube and its symmetry group one can get a set of related polyhedra via adding congruent pyramids to its faces. The height and the rotation angle of the added pyramids give rise to a two-parameter set of such polyhedra. Thereby occur Archimedian solids and their duals, as e.g. an “icosi-tetra deltahedron”, but also starshaped solids. This approach can also be applied when taking a regular tetrahedron or a regular pentagon-dodecahedron as start figure. A hypercube in $$ {\mathbb{R}}^{n} $$ (an “n-cube”), too, suits as start object and gives rise to interesting polytopes (c.f. [1–3]). The cube’s geodesics and (inner) billiards, especially the closed ones, are already well-known (see [4, 5]). Hereby, a ray’s incoming angle equals its outcoming angle. There are many practical applications of reflections in a cube’s corner, as e.g. the cat’s eye and retroreflectors or reflectors guiding ships through bridges. Geodesics on a cube can be interpreted as billiards in the circumscribed rhombi-dodecahedron. This gives a hint, how to treat geodesics on arbitrary poly-hedra. Generalising reflections to refractions means that one has to apply Snellius’ refraction law saying that the sine-ratio of incoming and outcoming angles is constant. Application of this law (or a convenient modification of it) to geodesics on a polyhedron will result in trace polygons, which might be called “quasi-geodesics”. The concept “pseudo-geodesic”, coined for curves c on smooth surfaces $$ {\Phi } $$, is defined by the property of c that its osculating planes enclose a constant angle with the normals n of $$ {\Phi } $$. Again, this concept can be modified for polyhedrons, too. We look for these three types of traces of rays in and on a 3-cube and a 4-cube.

Duality occurs in pairs of polyhedra, for example between the icosahedron and the dodecahedron, between the cube and the octahedron, and self-dually in the tetrahedron. In this paper, the principle of duality is generalized and linked to the construction of alternating knots. In a polyhedron, each surface has at least three vertices and there are at least four surfaces. There is always a dual polyhedron. From both, an alternating knot (or link) can be constructed, one that has as many crossing points as the polyhedron has edges. It turns out that this result also applies to bodies whose surfaces have less than three vertices and which consist of less than four faces. The resulting bodies can not be assembled like polyhedra from flat faces. In the following, they will be referred to as “polyliner”. If each facet has at least two vertices, an alternating knot can be constructed as before. If facets with only one point are present in the polyliner, the construction of the associated knot at this point results in a loop that can be unknotted. If the disentangling is not done, but the crossing point is maintained, then the resulting spatial curves can be cataloged according to their topology.

Graphic constructions of real three-dimensional quadrics as cuts of four-dimensional cones with three-dimensional spaces are described. All the constructions are presented on interactive models in GeoGebra 5 with use of descriptive geometry methods, which are based on a visualization technique of double orthogonal projection of the four-dimensional space onto two perpendicular three-dimensional spaces. We visualize a four-dimensional cone, its cutting 3-space and the section simultaneously in one figure. For detailed reasoning and verifications, the constructions are also supported analytically.

During the seventeenth century, several Neapolitan churches were built or renovated according to an oval planimetric layout, including: San Carlo all’Arena; San Sebastiano; Santa Maria Egiziaca a Forcella; Santa Maria di Caravaggio. The study method starts from the churches architectural survey and provides the plant and dome curves and surfaces geometric analysis with 3D modeling. The goal is the churches graphic analysis to define analogies and differences. From a formal point of view, a flat ovate shape is characterized by a curvilinear profile with double orthogonal symmetry. From a geometrical-mathematical point of view, it can be circumscribed either in a polycentric curve (ovate shape is a flat figure generated by the succession of several circumference arcs, whose contact points must satisfy the continuity property) or in an ellipse (geometric place of the points of the plane satisfying specific relations). The restitution and analysis of the three-dimensional geometric model is realized with a commercial application software for the 3D modelling of sculptural surfaces or ‘free form’. The ovate matrix is the configurative origin of the entire spatial layout. The elliptic curve, which approximates the planimetric profile obtained from the survey, has been assumed as a dimensional model and genesis of the three-dimensional modelling of the church. The spatial layout of the church can be traced back to a geometric model composed of a straight cylinder and a dome.

The authors classify the relationship between toy blocks with patterns that comprise optical illusions and architectural theory. They confirm the latter explains the phenomena about the former: especially remarkable is the phenomenal transparency that applies transparent physical layers to optical phenomena with virtual layers. They describe notable essences of the phenomena around the blocks in its depth in our vision and wide-angle effectiveness. These essences account for contemporary tendencies in architecture: semi-transparency after realizing a complete transparency and frequency of change in its appearance. These tendencies are partly realized by technical inventions but the authors emphasize its basis on the formal and spiritual properties in our age referring to examples with relatively low technology. They require mainstream architectural theory in modern times to be revised in historical and aesthetic points of view, though its involving issue of equivocalness of the message on a surface in architecture. They possibly stem the trend for transparency in a broader modern times with turning architectural surface to the place of expression with transparency and opaqueness, and raise a question about a cityscape filled with different buildings and monitors in terms of aesthetics.

Linear perspective is regarded as the approximate mathematical-geometrical translation of human visual perception on a two-dimensional surface. However, blind people cannot take advantage of the sense of sight and they consequently have no direct experience of perspectival illusions typical of vision. Ever since the Renaissance, a significant proportion of Western painting has been characterized by the meticulous implementation of perspective but its two-dimensional nature makes it impossible for a blind person to truly and genuinely appreciate such an invaluable heritage. Is it possible to recognize the value of a painting by Paolo Uccello or Piero Della Francesca without acknowledging the role played by perspective in them? In a world that is becoming increasingly inclusive, it is unacceptable to deny an entire—though small—category of users the fruition of artworks in which the comprehension of how the rules of perspective define space and composition is inextricably bound to the understanding of their profound meaning, especially when we relate to a universal language like art. This paper tries to reflect on the possibility to fill—at least partly—the existing fruition gap between sighted and blind people that currently characterizes most part of communication strategies for pictorial artworks, especially in museums. The traditional techniques of Descriptive Geometry, like photogrammetry and geometric restitution of perspective applied to painted spaces, combined with the use of new technologies (ICT), like 3D printing, can be crucial in the scientific translation of painting’s two-dimensional spaces in three-dimensional models which can be experienced through touch and other senses. Moreover, the multisensory approach becomes an opportunity to enrich knowledge also for sighted users: such an alternative way of experiencing art is able to transmit new significances and allows forms identification by avoiding the extremely crowded sense of vision.

The aim of this work is to present a progress of the main research master’s thesis author “Hangeul. The systematic of the writing systems in generating new spatiality”. The writing systems emerged as revolutionary procedures. The societies think them, not only, as original techniques for preservation of traditions, they also give them cultural identity patterns. The Korean writing system called Hangeul is a particular alphabet. It is recognized and registered in the Memory of the World—UNESCO—but is not limited to the field of linguists. Its graphic expression is one of the principal characteristics. Their letters, based only on pure geometry, are drawn quickly and simply. They are designed to be drawn with continuous strokes and based on a square structure. The signs of the Korean alphabet are based on five elements, that is, basic morphological units: points, circles and horizontal, vertical and oblique lines. The experience that is part of the research project Master’s thesis “Hangeul. The systematic of the writing in generating new spatialities” developing by the author that investigate spatial formal explorations into the cutout of the entitative morphology, establishing the systematics of the Korean writing system (Hangeul) as possible starting point of projective processes. The research explores the approaches in analysis of forms cut out of entitative morphology, each sign of Hangeul become the starting point for an initial translation of basic geometric component to design and study the projective logics that establish a conceptual process of translation of the Korean alphabet as source text, as the basis and support of projective processes of forms and spaces.

This work deals with a novel procedure that can be used for reverse engineering (RE) of big and old boats’ hull through cheap and effective instruments. The procedure has been used to acquire dimensions and shapes of an offshore boat designed by Renato Levi in 1962, named “Ultima Dea”, commissioned by Gianni Agnelli. The research purpose is the development of a method that gives to designers and restorer an “easy to use” instrument for obtaining the 2D and 3D CAD models from a degraded physical object in order to check and re-design the parts to be restored. The study and the application allowed to develop an innovative procedure to set the right acquisition parameters for optimizing the RE output in terms of minimization of maximum error and mean geometric errors between physical object and virtual model, by using a one-shot RE operation and a completely off-line post-processing. This procedure ensures good timesaving, during acquisition, very high reliability level and lightness of CAD models, also being able to reconstruct worn down and spoiled parts (through ex-novo modelling). The procedure shows how the CAD-modelling step can be done directly on graphical models (without surfaces’ mathematics) while ensuring the appropriate level of detail and, contemporarily, improving the interoperability of used and developed software. This procedure is based on the use of well-known methodologies and instruments that usually are employed in architectural relief; finally, it allowed to model the boat’s hull for the redesigning of engine/electrical/services systems and to restore the boat completely.

This paper aims to analyse the representation issues related to the design of residential and industrial landscapes in Piacenza, along the Trebbia River. From the survey stage to the representation time, we want to recognize the landscape with geometrical signs, connecting lines, first of all underline natural signs of the land, coming from geographical maps, discovering a possible natural and agricultural measure and orientation between new and old geometries of the Pianura Padana’s landscape.

A series of geometric and visual researches—originated from centuries by the need of cartographic and cosmographic planispheres reached up to the analogical graphics of the recent twentieth century drawing works of M. C. Escher have patiently elaborated the hermeneutics of a visual culture and consequent technology that makes us today the customary language used for digital spherical cameras. At the same time, the virtual reality interactive viewers, or augmented reality smartglasses, allow us to access, trough functional metadata, the digital files of 360° spherical images with the same gestural immersiveness of environmental orientation usually used to orientate us in real spaces. After some complex prototype, are now available some prosumer models of qualified spherical cameras, and even other hi-level multicamera systems. The performances of the softwares recently developed for the matching of this kind of panoramic pictures are progressively improving, even in form of app for smartphone cameras. After hundreds of shootings on the field, in this manuscript are described some case studies about interiors of architecture (indoor) and open and complex urban landscapes (outdoor), exemplifying the more appropriate management of perception of circular perspective for the architectural immersive representation, even to represent complex contexts in the simple and flat rectangular panoramic format. The technical debate highlight how in our visual culture is going to be progressively accepted a paradigm a of an exceeding digital iconography that include not only a linear perspective, but even a spherical representation of the full surrounding visual space: a point of view, even metaphorically, centered on the value of the observer: standing between the micro and the cosmic dimensions, and in the fulcrum of Science and Art.

In medieval churches motives are found, similar to what we call today “Sierpinski triangle”: a same composition of full and void areas, interweaved and repeated at smaller and smaller scale. The motive has seen its mathematically rigorous definition in 1915, and has been a “benchmark” for scientists thereafter. Mathematicians imagine and study what would remain upon carrying on indefinitely the procedure of inserting voids: a “powder of points” would be left, organized in a precise way around large voids. On the other hand, the geometrical compositions of the Marmorari Romani, loosely known as “Cosmati”, are often characterized by repetitions on different spatial scales, thus suggesting to the spectator an in-depth view (Moran and Williams, Boll. Mat. Ital. Sez. A, ser. VIII, VII-A:17–47 (2004), [22, Williams in Math. Intell. 19:41–45 (1997), 30]). Actual artifacts composed iteratively can be reliably analyzed with mathematical methods, if the motive shows at least three levels of iteration (i.e. different spatial scales). In Conversano and Tedeschini Lalli Aplimat (J Appl Math 4:113–122, [10]) we reviewed some such triangles, in stone, isolated in medieval floors. In the present paper we report about some new examples recently found in Rome, and not published yet in any form. These are isolated Sierpinski triangles in golden leaf, contained in the frieze of medieval cloisters. Their composition is iterated at 3 and 4 levels. Moreover their placement warrants to their authenticity. Where the stones have fallen out, empty lodgings along the frieze testify that it has gone untouched for a long time. The “protagonists” of the motive are the smallest stones, as they are the ones in golden leaf, i.e. all that is perceived when looking up. Moreover the golden leaf reflects the light, adding the perceptually smaller spatial scales of the shimmering.

Dues to the electronic resources are stored and edited individually in the web-based distributed environment, how to manage these massive unstructured resources so as to construct an efficient and flexible data environment are the urgent challenges for cooperative applications. Therefore, a storage model of resources management platform is proposed for collaborative editing and learning applications. At first, a logical storage structure based on concept tree is constructed, so as to organizes and manages the electronic resources with association. Then a cloud storage mechanism based on Hash Table aiming at massive resources management is given for storage of distributed resources. At last, a porotype is developed for a web-based learning application. It is shown that the storage model can effectively support large-scale web learning applications.

Despite the worldwide popularization of computer-assisted drawing programs in all their variants, the Representation Systems used to develop projects in Architecture have changed very little or nothing. Based on Descriptive Geometry for 200 years, in practice there is no renewal of space conceiving nor in the way objects are organized and distributed in relation to it. These systems ignore by default all the dynamic, immaterial, sensitive, random, ephemeral and changing components of the architectural project. An Unlikely Rome reveals, together with the Intersemiotic Translations and Drawings by Machines, a certain gap in Representation, which cannot be saved through the use of CAD based programs. This work confronts us with the complexity of the world on the one hand, and with the capacity of our minds to make decisions in the field of abduction on the other. The goal of this work is to innovate in the Generation of Architectural Space through a process that involves changes in Representation as well as in the generative processes in Architecture. This means treating each difference or alteration as unique without falling into generalizations or simplifications. Representation and Geometry are, overall, defined by what they hide. Let’s search, though. An Unlikely Rome starts from a Non-Representation of the city of Rome, hidden behind its own Representation. The reconnection of the nodes through an abductive process provides creative, not programmable by computer, systematic, complex new answers.

Cellular automata are models that deal with both nature and artefacts: they can indeed simulate living beings as well as be employed in the creation of objects. After the introduction of this concept by Stanislaw Ulam and John Von Neumann in the late 1940s, many different kinds of cellular automata have been created and have become part of what Christopher Langton called “artificial life” in 1986. The most complex examples among them are based on stochastic development, thus they share their structural properties with morphogenetic models like the one suggested by Alan Turing (1952). This is the reason why some cellular automata are capable of simulating the development of living beings, but also of cities and artefacts. They are indeed widely used in computer graphics related to parametric design, in order to create performative objects at various scales that can be produced according to the principle of mass customisation. The purpose of this study is to analyse the properties of these models with the help of computer simulations and, as a consequence, to explore some of their different fields of application. As a result, it can be observed that these processes, based on a stochastic geometry, can lead not only to simple biomimicry (regarded as the artificial replication of biological features) but also, in a wider sense, to bioinspiration (a more general relation between nature and artefacts based on shared structural properties).

This paper sets out to paint a portrait of applications and trends in interactive and smart solutions designed to use a multimedia educational approach to foster and promote CH. It is increasingly important in the field of cultural heritage, museums and exhibitions to facilitate learning by encouraging visitors to interact directly and physically with the heritage on display, and current research seeks to identify engaging strategies and means to communicate cultural messages. Some projects focus on the physicality of tangible interaction thanks to innovative interfaces and technology embedded in objects, while others engage users in moving their whole bodies or making simple gestures to interact with digital and multimedia content and break down the barrier between the physical and the digital. The case study outlined here describes an interactive exhibition on the world of Renaissance genius Leonardo da Vinci in which visitors interact with a life-sized holographic projection and have the impression that Leonardo da Vinci actually sees them and decides to entertain them with short anecdotes from his life, recounting his work and relationship with nature.

This paper aims to investigate the conditioning that the use of playful games requires the role of graphic element for disseminating and promoting the Cultural Heritage. Within the CHROME project, which has, among the various objectives, the definition of an innovative strategy to promote the three Charterhouses of Campania, it comes up with the idea to plan a playful game placed in one of the three monasteries. Its purpose is to provide a first knowledge, both in relation to the spatiality of a Carthusian monastery and to the life of a monk of the Order, exploiting the playful dimension of the games. Since that the proposed location for the game is a monastic complex whose modeling is gained by range-based and image-based survey processes, the project shows the definition of a methodology to generate digital three-dimensional models, whose geometric genesis is at the same time both topologically coherent and enjoyable on the selected technology platform. Once obtained the scene in which the narration develops, it must qualify as a visual device able to activate the sensory involvement, the share and the exploration. For this reason, some expedients (illumination techniques, framing, distortions, sonorous scenes) have been studied to stimulate the player and to communicate cognitive messages related to the game space using the principle “show, don’t tell”.

Traditional Arabic ornaments highlight their complexity of graphic drawing through two-dimensional geometric matrices, based on elementary forms and regular polygons, with developments and hybridizations of ornamental motifs, calligraphic inscriptions and naturalistic symbols. The excellence achieved by Moorish civilization is Spain distinguishes Andalusia for valuable decorative apparatuses within architectural environments, among which court halls and private rooms of Alhambra complex in Granada, where many researches and studies on shapes and geometries were developed. The presented research contributes to the investigation on geometric decorative apparatuses of Alhambra, in relation to the experimentation of 3D documentation and representation systems for the analysis and cataloguing of geometric patterns, within a joint multi-year research project on Alhambra complex between University of Pavia and University of Granada (scientific directors: prof. S. Parrinello, prof. A. Gómez-Blanco Pontes), applied into Generalife Palace. Digital survey methodologies are applied on decorative surfaces, imposing an accurate scale of surface analysis; as 3D entities, the documentary approach is not limited to 2D survey but developed within virtual models of patterns through polygonal surfaces obtained from Range-based and Image-based surveys. The experimentation of virtual reconstructions of ornamental bas-reliefs allows the comparison between ideal models, obtained with parametric surfaces from geometric matrix, and real prototypes, from triangulation of measured points, evaluating complexity of geometric surfaces represented by multiple levels of shapes. The research, began in 2017 and currently on course, aims to extend the survey to the entire monumental complex of Alhambra palace.

Serbian medieval architectural heritage is notable for its sacred architecture including numerous Christian Orthodox churches built at the territory of former Raška state during the period from the 12th to the 14th centuries. Built in the so-called Raška architectural style, characterized by overlapping features of Romanesque and Byzantine traditions, two monuments—the church of the Mother of God in Studenica monastery complex and the church of Holy Dormition in Žiča monastery complex, are exquisite sacred structures and cultural monuments of exceptional importance. They are also remarkable due to geometric-proportional regularities of their design. This paper highlights the importance of geometric concept in relation to proportional analysis of these two structures. Here presented study is conducted by two means: first one—by investigating geometric scheme with equilateral triangles, incorporated into the layout and cross section patterns of each church structure; the second one—by classical proportioning that includes proportional roots, golden section and numeric ratios.

The present work describes a methodology aimed at identifying the theoretical shape of a dome, as conceived by the architect. To this purpose, a novel analysis procedure has been specifically developed to verify the correspondence between the real shape, obtained by a survey, and the geometric one, derived by architectural treatises, when possible. Actually, the common practice of analysing just one profile of a dome is not sufficient to characterize its entire surface since domes often display asymmetries and deformations; this implies that the selected profile may not always be representative of the entire surface. On the contrary, with the best-fit 3D surface analysis here proposed, it is possible to check the overall dome geometry. In fact, the iterative best-fit process enables to determine the axis and the inner profile of the geometric dome, within a fixed accuracy. The study consisted in two phases: (i) data collection by high precision survey with 3D laser scanning technology; and (ii) data analysis, according to both a geometric and analytic procedure. The results obtained by the two procedures were compared in terms of accuracy and computing speed. This dual methodology was applied to the dome of Catania’s Cathedral, built after the 1693 earthquake and completed in 1802.

As the advantages of foldable or deployable structures are being discovered, research into origami engineering has attracted more focus from engineers. With computer aided design and parameterized modeling techniques, some computational origami design methods have been developed. Most of these methods focus on the problem of origami crease pattern design—the problem of determining a crease pattern to realize a specified origami final shape, but do not provide computational solutions to actually developing a shape that meets some design performance criteria. This paper presents a parameterization method of unit cell for N-1 type base patterns. Then, a computational design method of polyhedron sandwich structure is proposed and the polyhedron sandwich structure will be designed to satisfy geometric, functional, and foldability requirements. All parameterizations are validated by comparison with physical prototypes and compiled into a MATLAB Toolbox for subsequent work.

Fiber-reinforced plastic (also called fiber-reinforced polymer) is a composite material commonly used in aerospace, automotive, marine and construction industries. It is found in ballistic armor as well.　Fibers such as glass (in fiberglass), carbon (in carbon fiber-reinforced polymer), aramidor basalt are usually used in FRP. Other fibers such as paper, wood, or asbestos are rarely used. In FRP, polymer is usually epoxy, vinylester, polyester thermosetting plastic, or phenol formaldehyde resins. This paper presents a process on test-manufacturing FRP parts from their CAD data, through which large and strong curved-shell type models or real parts can be produced more quickly, more precisely and more economically than rapid prototyping or 3D printing methods.

To ensure Cultural Heritage preservation it is necessary to understand its level of structural safety. When it comes to buildings with complex geometries, however, it is not easy to give an answer to this need: the current methods, require numerous inspections, time and economic resources. The goal of this study is to understand how to deal with the preliminary static study of an existing complex structure, starting with already available traditional 2D surveys. It is possible to achieve a 3D restitution of a building with a correct use of simple geometrical and graphic rules and with the help of the most common modeling digital software. The method works with various survey typologies, with increasing precision, but the descriptive geometry is that used originally, and brings with it the design idea and the original proportions. The method is applied to the apse of the Duomo of Milan, but is extendable and can be generalized for many buildings characterized by complex systems with arches, vaults and domes. The differences between the so represented ideal structure and the constructed real structure may be negligible for the purposes of the static analysis for which the method is used. The three-dimensional representation allows to derive the volumes and the weight of the construction elements and through the static method of limit analysis it is possible to study the structural response. In the case analyzed, the adequacy of the geometrical layout and the soundness of the structure designed 630 years ago has been demonstrated.

In this work, modelling of 3D jets without any fictitious values is discussed. At first, free axissymmetrical jet is analysed. The approach is based on theory of A. Tkachuk, the Professor of Heat Gas Supply and Ventilation department of Kyiv National University of Construction and Architecture. 3D jets contain large-scale vortices (puffs), which can be represented as spheres. In ventilation technics, the same equations are used for wide range of Reynolds number. Thus, the picture visualized al low Reynolds number can be used for ventilation jets, which can be represented as spheres growing and rolling on the jet boundary. X-velocity inside a sphere can be found by the Euler’s equations for rotation. Between the puffs, the velocity is approximated with smoothness conditions of velocity profile. Average velocity can be found by integration. The results good coincide with known velocity profiles such as Schlichting’s. This allows wide implementation for complex jets.

This paper uses a formulation of the motion of the planar four-bar mechanism in the projective three-space of planar kinematic mapping and an algebraic version of the input-output relation is derived. This fourth order algebraic curve describes a new convenient form of the Freudenstein equation. Different geometric properties of the curve, independent of the design parameters, are carried out and their impact on the topology of the mechanism is shown. Furthermore the coefficients of this algebraic input-output curve are interpreted geometrically in the design parameter space which yields regions of parameter sets to the different topologies of four-bar mechanisms.

Navigation in urban public spaces has proved to be very important factor in creating public life in public spaces. Tracking people movement in most of the studies was done in situ, limited by a small sample of respondents, and the processing of this data was exhausting and long-lasting because it comes down to manual work. On the other hand, virtual environments represent an ideal test site, as the researcher has complete control over the environment. This paper will deal with the method of collecting and processing data about the pedestrian movement through virtual urban space and visualization of these data in parametric software in order to get relevant quantitative sample.

There are many examples that represent a profound link between architecture and writing. Both “visual languages”, the two systems have historically interacted, reinforcing each other and activating multiple visual relationships related to the different cultures and linguistic areas. In this very broad context, the paper develops a particular reflection on the relationship between architecture and writing through a particular case study: some of the many small funerary buildings constructed between the second half of the 1800s and the beginning of the 1900s in the Campo Verano cemetery in Rome. This is a readily circumscribed area referring to the relationship between architecture and writing in Western culture and the use of the Latin alphabet, mostly with capital letters, for the necessary specifics that such a study entails. The area is limited, but is functional for investigating the relationship between architecture and writing. Through the means of graphical/geometrical analysis, it has allowed a useful method of investigation to be developed to understand this architectural heritage, which is extremely interesting but particularly complex to decipher.

In order to better understand the distribution of dissolved oxygen and the nitrogen in the Fuzhou River Constructed Wetland and to take measures to increase the removal rate of the nitrogen, visualized analysis is carried out to show the distribution clearly. We use the Kriging and the Inverse Distance Weighting method of ArcGIS to interpolate into the dissolved oxygen and the nitrogen from the plane, transverse, and lengthways direction of the wetland. Then the dissolved oxygen and nitrogen content of the wetland can be visualized, based on which the relationship between the dissolved oxygen and the nitrogen can be analyzed more effectively.

With the increasing needs of the exterior design of the complex machinery product design, the collaborative design between the structure design and exterior design are required, thus, this demands the exchange of the model files between them. The process of the appearance and image design for complex mechanical products is analyzed. Focused on two steps of the design processes: import the former structure model to the design software as a design reference model firstly, secondly, the multiple iterations and adjustments of the appearance model and the structure model. Moreover, the modeling converting methods between the engineering software and industrial design software are investigated. By analyzing the advantages and disadvantages of several model conversion intermediate formats, the method of model optimization derivation is shown: according to the characteristics of the different features of models, the different importing methods are used. Finally, the method of modeling converting is validated.

This research provides initial examination of the impact that biomorphic forms, implemented in public space as urban design model, has on its potential users. The methods, which were included in this research, was modeling process of biomorphic form of species Bell flower (Campanula persicifolia L.) into urban design model of bench and a visual questionnaire for examination of the visual perception from two target groups. The visual research was based on a validation of a frequently used urban element—bench, on the original photo material which was taken at the city of Belgrade, and a photo-realistic material. At the photo-realistic material, the original urban element was removed by the conceptual model of bench constructed from the biomorphic form. Evaluation of two photos in the visual questionnaire included five criteria that rely on visual capabilities of user’s free assessment and user’s ability for visualization: (1) harmony, unity of space; (2) the legibility of the form of the elements; (3) comfort, amenity; (4) design of the element and (5) innovativeness, attractiveness. Categorical scale was used for assessing quality of criteria by subjects: EXCELLENT, GOOD and BAD. Results of the visual questionnaire indicate that the biomorphic urban design model was generally considered to be excellent and of innovative design, compared to the standard urban model. This innovative urban design model of the public space could be the part of a new approach that has been trying to find a new ways for connecting people with nature and its hidden patterns and forms.

The study elucidated geometrical consistency among the architectures designed by Aldo Rossi (1931–1997), and showed the connection geometry and what he called “analogy”. In view of analogical connection, Rossi repeated ‘Triangle Fountain’, defined as geometrical compositions of triangular prism in his realized architecture. In order to define what caused analogy to connect his architectures, the study specified several “Triangle Fountain” in the entire of his architecture and simplified them to three types of geometrical diagram. One type was seen as “Lifted by Pillar” where the extruded triangular prism was lifted by supports. In the type, the triangular prism worked as bridge, where people or water go through inside. The second type was “Cantilevered”. In this type, one shorter triangular prism was on the wall, and water ran through from the wall and dropped into the cube drain. The third type is “Synthesized”, where Triangle Fountain was supported by pillar and wall. Despite several materials, Triangle Fountain gave consistency to his architecture. For the conclusion, geometrical analogy of the repetition of Triangle Fountains could be expressed as a geometrical formula, which showed the third type equaled to the first and second type. Like chemical formula of equilibrium, the repetition of geometry was rendered to another geometry enabled us to evoke another architecture in several sites.

This study aims to elucidate and situate the design of Chandigarh by Le Corbusier among his whole creative activities. To accomplish the aim I surveyed many documents related to Chandigarh. The result is as follows. On architectural and urban design: (1) His sketch attached to his letter to Yvonne with the date: February 26–28th, 1951, shows that his first image of Chandigarh was linked to the Himalayas and his first image of <birth>: a woman holding a baby. (2) I could confirm that his first city plan had a 7/7 square scheme based on an 800 m module. (3) He learned from Indian architecture as follows: (a) local properties: accommodation to Indian climate, (b) universal properties: grand cultures on a grand geometric scale. On pictorial images: (1) I could confirm that his first sketch of Chandigarh in his letter to Yvonne and another sketch with the date: March 3rd, 1951, had his first image of <birth>. (2) His serial sketches showing his second image of <birth> in Album Nivola 1 were linked with the first creation of Chandigarh, via a sketch among them with the date: March 1st, 1951. (3) The serial sketches were linked with <D3 fusion> of Poem of the right angle after the first creation of Chandigarh. Finally I could define Chandigarh as follows: it is not only the creation of a new capital, but the creative play of different images, crossing over the boundaries among different genres, brought together under the context (light) illuminating the place.

The demand for CAD models of the real world is constantly growing. Applications in different domains need adequate modeling. In this contribution, we describe how catalogue-based CAD models and point cloud data are represented by extended boundary graphs and use this representation to fit catalogue-based parts in a point cloud with a maximum common induced subgraph-matching algorithm.

The worked out modeling methods of topographic surfaces allow nowadays to reflect, with different degree of adequacy, the real characteristics of the subject modeling. One of the main applied tasks is representation of continuous topographic surface in digital form, using final memory volume. The well-known topographic modeling systems (geographical information systems) comprise various models—Digital Elevation Model (DEM), Digital Terrain Model (DTM) and etc. and they are oriented on complex variety of practical tasks solving. As a rule topographic surface modeling systems pursue the following common tasks: DTM model generation, DTM change and optimization, DTM analysis, DTM visualization, DTM and produced information rendering. The most part of DTM is being made on the base of one of two structural data types: regular network or TIN (Triangulated Irregular Network). The matters of choosing TS modeling method in a great number of existing methods are considered in this article. Different regularity criteria are suggested.

Stairs are important elements in architecture. After an introduction to the function, history and design rules of stairs, the studies of the geometry of stairs are in the focus of this research and educational project in architecture. The geometries of stairs can be related to their typologies and the resulted movements in space. Moving directions can be derived from the geometries of stairs. Of particular geometric interest are the various spiral staircases, single and multi-run or single and polycentric spiral staircases. With the help of their respective geometric concept of screwing different movements and fascinating geometric objects are the results. Finally, the kind of movements on stairs related to the inclination is the theme of the sinus stairs. The sinus stairs offer, with continuously changing step height and step depth according to the sine curve, smooth movement, as if walking onto a natural hill. A sinus staircase had been built by the students in a walk-in project in order to test the thesis. The stairs with their geometries had been analyzed by 3D-models, drawings and physical models.

Artists, philosophers and mathematicians coming from different historical eras reflected on the proportions and symmetry of the solid forms, adopting the five regular polyhedra as elements of the highest expression of earthly and celestial order and perfection. The knowledge of these eternal archetypes of perfection, followed by semi-regular polyhedra and their combinations, became essential in treatises, especially during the Renaissance. They appeared on the frontispieces of texts to justify the scientific reliability of the texts themselves and, more importantly, they were favoured models on which to demonstrate the perspective technique to obtain a clear and intelligible two-dimensional image of their spatiality. Nevertheless, not only a graphic evolution but also the demolition of their eternal balance is clear while browsing the many illustrations of regular polyhedra and their derived shapes. In line with the historical-artistic events of the post-Renaissance era, the regular polyhedra, gaining obsolete and “dangerous” positions, are overwhelmed by an imagination which explores aesthetic opportunities and offers the observer attractive and endearing images. In response to this evolution, the French Minim friar J. F. Nicéron (1613–1646) offers his “version” and spatial articulation of the regular solids on the edge between the rigour of the Italian perspective tradition and the new Northern European trends. The author consciously tried to break the archetypal aura of immutable shapes to reveal, to the trained eye, not only a playful element, but also a faithful adhesion to the poetics of the Cartesian doubt, on the edge between scientific rigour and taste for wonderfulness.

To create calculation model easily and efficiently can essentially reduce time cost. Currently, lots of visual modeling programs have been developed based on different CAD systems. In this article, the developing idea of a visual modeling tool based on field oriented development was introduced; Considering the feature of physical modeling, fast and convenient operation modules were developed; in order to solve the storage and conversion problems of large-scale models, the data structure and conversional algorithm based on the hierarchical geometry tree were designed; several functional modules were developed, which can provide the template of the complex model components and material parameters; The automatic conversion and generation of physical model input file for some MC codes. By using this modeling tool, some reactor whole-core physical model was created, and the transformed file was delivered to MC code for transport calculation. The results were compared and validate the correctness of the visual modeling tool.

The paper intends to highlight the links between two-dimensional geometric matrices and three-dimensional structures in Andalusian architectures of Islamic origin. The deep ambivalence between plane and spatial geometries maintains a very strong evidence, for example, in the flat projections of the articulated vaulted surfaces ribs or the muquarnas cellular structures. The creative process underlying the geometric grid systems of these shapes is based on analogous proportioning systems and geometries, underlying the plane patterns. This article then analyzes in particular the geometrical principles, the transformations and the design aspects that were used to create the modules of the flat decorations and how they can be understood as structural schemes for the architectural buildings. To this end, some emblematic buildings of Islamic architectural production in Andalusia were examined, focusing on the most significant dome structures. In these it was possible to highlight how the purely ornamental aspect linked to the geometric design, constantly interacts with the architectural form.

This paper introduces an extended morphological closing operator so that global structure of objects is considered. Our method computes the original closing for local regions of the object, and composes the closing results. Main idea is to define the local region by geodesic distance from the target points. This enables us to preserve global structure of the input objects while filling local holes. In addition, various level of structure can be extracted by threshold control. Moreover, opening operator can also be defined by the proposed method.

A prototype hybrid machine was manufactured by combining five-axis laminate-shaping and five-axis cutting, and a CAM was developed for additive manufacturing under simultaneous five-axis control. Using a CAD surface as a shape-model for the laminate-shaping, the reproducibility of a shape in laminate-shaping or cutting was successfully enhanced. Moreover, a combination process of laminate-shaping and cutting was successfully defined by decomposing a shape into multiple parts. The hybrid machine and CAM developed were investigated in a case study, and their usability was confirmed.

When we draw lines and circles, we do not draw them at random. We look at the 2D figures carefully, and think what drawing method to do next. Namely, we think we should use a drawing compass or a ruler. We have two or three choices at drawing. In this study, we tried to seek drawing methods automatically. It is known that Prolog programs are preferable to select from some choices. Two programs were made in Prolog. One program is to seek a perpendicular line; under the condition that one line and one point on the line are given, and by drawing same size circles. This program has 500 lines in Prolog. The other seeking program is to determine a perpendicular line by drawing different radius circles. The radius of the drawing compass can be changed infinitely; we restricted two different radius lengths. These programs can seek perpendicular lines. In the future we want to apply to more complicated drawing problems such as ones in descriptive geometry.

It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space $$P^3$$ and all real points of the so-called Plücker quadric $$\varPsi $$. Moreover one can identify each point of the Plücker quadric’s ambient space with a linear complex of lines in $$P^3$$. Within this paper we give an alternative interpretation for the points of $$P^5$$ as lines of an Euclidean 4-space $$E^4$$, which are orthogonal to a fixed direction. We study straight lines in $$P^5$$, which correspond in the general case to cubic 2-surfaces in $$E^4$$. These surfaces are geometrically connected with circular Darboux 2-motions in $$E^4$$, as they are basic surfaces of the underlying line-symmetric motions. Finally we present an application of this interpretation in the context of interactive design of ruled surfaces and ruled surface strips/patches based on the algorithm of De Casteljau.

This study presents a prototype of an augmented reality (AR) mobile application aimed at visualizing infants’ natural-setting motor and cognitive development for prevention of accidents and promotion of development. To provide adults with better understanding about the infants’ encounters with surrounding objects by visualization of actual recoded data, the study comprised three steps. First, we conducted longitudinal observations of 10 infants (6 males, 4 females), aged 4–12 months, at their homes in Tokyo, Japan. Second, we developed an AR application for iPhones and iPads, by using vision-based marker tracking technique. Based on the observations, 10 most frequently observed objects were adapted as markers for AR. To ensure privacy and to focus on infant–object interactions, we converted all AR movies to line drawings. Third, we conducted informal user interviews and user tests to confirm the method’s validity and usability. The longitudinal observational data shed light on the infants’ perceptions and actions, helping to clarify not only developmental possibilities but also risks of accidents. The user interview suggested that our prototype could scope out the home from infants and can help adults to obtain insights for encouraging child development and reevaluating childproofing home as an ongoing process.

The aim of this research is to examine and outline modularity of the selected representatives of concave polyhedra of the second sort (C II), from the point of view of their high combinatorial potential for creating diverse polyhedral structures, some of which can be applied in architectural design. The modularity is primarily attributed to the regular polygonal bases around which the solids are created. There are three basic groups of concave polyhedra of the second sort: concave cupolae (CC II), concave pyramids (CP II) and concave antiprisms (CA II). Since each of these groups contains the representatives with octagonal bases, they are chosen for this research, not only because of their compatibility, but also because of their accordance with the orthogonal matrix underlying the conventional modular grid, ubiquitous in architectural design. In this study, we examine the possibilities of modular conjoining of these polyhedra into new, composite structures, creating forms that can contribute to enrichment of architectural design expression, allowing easy execution at the same time.

The aim of study was to clarify a character of “Architectural geometry” through analysis of contemporary architecture made of square plan.Results could be summarized in the following statements,1.Architectural geometry is defined as the three stratums: compositional geometry, projective geometry and signified geometry (non-Euclidean geometry).2.Architectural geometry is characterized by “Scale”.3.Examining the typological structure of the morphological composition of the contemporary architecture made of square plan by using multivariate analysis of compositional elements.4.Discovery of latent structures that define five types;a.Symmetry and Asymmetry of the compositional elements.b.Unity and Plurality of the compositional elements.5.Examining of character of types and transformation of the morphological composition with scaling.

The relationship between representation and the object represented is not unique since a plane figure can refer to an infinite number of spatial counterparts. In particular situations, this indeterminateness can generate optical illusions and visual paradoxes. This work analyses precisely those video games that exploit these paradoxes. As in an Escher-like environment, the spaces proposed in these applications confound visual perception, forcing the user to act according to unusual logic. In fact, the process of projecting a three-dimensional object onto a two-dimensional plane depends strictly on the centre of projection. This characteristic was used in the twentieth century to design impossible three-dimensional figures. These structures, while existing only in the two-dimensional world, were implemented in some types of video games that, using graphical expedients, made the surfaces possible to travel virtually. This study categorizes these video games based on the projective method used and a schematization of the type of recurring paradoxical environments.

Architecture, being an inexhaustible source of ideas for shaping both interior and exterior, is in high demand of the development of novel methods for geometric form generation. Nowadays the architectural objects, in regard to high degree of computer design and material technology development, are realizing as complex geometrical structures. Directorial surfaces are created on the basis of the specific set of rules, being a locus of points in space with the constant either sum of distances from predefined line directors. In this paper we derive the mathematical model for the particular directorial surfaces’ generation which seems to be suitable for cupola design. Representative Serbian buildings are analyzed and the possible reconstruction of their cupola are suggested.

In this paper, we present the research conducted at the Autonomous Metropolitan University, in Mexico City, which consists of a new method for modeling, in three dimensions, the parts of the biological form of small-scale animals. For this study, we worked with the Green chinche (Nezara viridula) that belongs to the Insecta class of the Pentatomidae family, which measures 18 mm long × 10 mm wide. To model the body of the Green chinche, were used: a series of five photographs. The technique of geometric morphometrics to find the numerical values of the coordinates “x” and “y” of the morphological points called “Landmarks” (points of reference). Three computer programs© to find the numerical value of the coordinate “z” of the points in space. In addition the elements, the point, the line and the planes in the space of descriptive geometry. This method demonstrates that the quantitative descriptors of shape and size in 2D help to model the biological forms of small-scale animals that can be printed in 3D.

Developing from researches on heterogeneous modelling and voxel-based design, as well as on digital materials and discrete assembly, the paper describes current developments of Wasp, a software tool for hierarchical discrete modelling of objects as aggregations of modular parts, with focus on the generation of architectural objects. By conceptualizing the discrete nature of the final objects already within the software, it becomes possible to model heterogenous artefacts composed of basic parts, which are reversibly joined into a complete aggregation. Within such framework, users are provided with different aggregation procedures to select rule sequences producing the desired outcomes, as well as basic utilities for part collisions avoidance, visualization and editing of the produced geometries. To increase control over designed objects, the framework has been extended to include hierarchical modelling with multi-resolution parts, more advanced generation and editing functions for voxel fields, multi-channel scalar fields and global constraints. Overall, the aim of the framework is to allow modelling of objects as aggregations of discrete units with reversible connections, hence allowing the production of architectural entities which could be assembled, disassembled, and reconfigured during their lifecycle.

The study focuses on the application of the Digital Surface Model (DSM) for the visualisation of a city and urban analyses. The DSM is a cloud of points on a regular mesh derived from the airborne scanning (ALS/LiDAR). The accessibility of data is growing and the production cost decreasing. The current scanning precision is sufficient to present buildings including architectural details in the scale needed for urban analyses. Although the DSM can be easily presented at the cloud of points, it is insufficient to make full visualisation of a city and a number of urban analyses. To this end, it is necessary to be able to examine visibility while taking into consideration that facilities may obstruct each other views. In this context, the paper introduces a method of geometric representation and computation of DSM as full 3D-mesh. Key issue is the huge size of such a model, which is a challenge for processing. Results possible to achieve are discussed and they are compared with other types of models (like CityGML, reality-mesh-models). The research was implemented based on software (C++) developed by author. It enables to process areas of the city up to 180 km2 in DSM resolution (50 cm grid) for the purpose of urban visualisation and various urban analyses.

In this paper, we propose a method of presenting images based on an unexperienced viewpoint. Production of images based on unexperienced viewpoints was done using equipment such as 360-degree camera and drone. The photographed image is intended to produce a picture that would not be experienced when a human being lives normally, suddenly encounters a big creature larger than himself, and performs a production that feels the danger of life it was.In the experiment, we did not give detailed information on the video, asked the user to watch the experiment video produced by the HMD, what kind of things he fears, what kind of thing is about fearing feeling, and evaluated by questionnaire survey whether we have seen such images so far. As a result, by selecting night from the evening in the situation of the surrounding environment and moving in the depth direction while fixing the gazing point at the center of the screen, we can feel fear and immersion, and as a result I was able to amplify the sense of tension not to get tired of viewers.

Generally, there are two alternative design approaches: top-down and bottom-up. At present, the skeleton top-down design has been widely studied, but it is too abstract and not easy to grasp, and meanwhile often ignores the application of existing resources and the role of the location and features of the parts in the design of related parts. In addition, the bottom-up design is detached from the design layout, resulting in low efficiency. To solve the problems, a modular middle-out design method based on 3D multi-body is proposed. Firstly, in accordance with structure characteristics of different kinds of products, types of multi-body layouts are described, and layout approaches are introduced briefly. Then, the most important issue of parameter correlation in middle-out design is discussed in detail, and subsequently on how to embed the design results generated by the design accelerator into the smart layout part is explored, so the reverse design idea is realized due to the terminal design requirements control the front-end design. Consequently, the correlation between dynamic characteristics and structure as well as parameters are created effectively. Finally, combined with the typical design case, the application of middle-out design method is illustrated. The result shows that the middle-out modeling approach is feasible and effective.

Statistical data on European productivity in the field of architecture and construction indicate the fact that digital techniques in the last ten years have unfortunately not contributed to increase productivity, such as it is the situation in most of the other industries. If we compare other branches of industry and the dramatic impact of digitization on increasing their productivity, the question arises. Why is there no such progress in the field of architecture and what steps are needed to increase productivity? In the last four years we tried to address the topic digital technology and non-standard architecture within the bachelor course “Design of specialized topics” focused on the material wood. We offered our students the chance to witness the whole process from the early design to the final construction on site with all the advantages and drawbacks of the matter. With the projects realized with our students we want to show the possible and efficient realization of objects with high geometric complexity. We also want to point out the need of a well-organized work flow which has let to remarkable results. The specificity of our projects is that a students’ competition, the planning and the building of the project take place within a single semester. In the paper we will give a short overview of the projects and we will point out the importance of the included geometry especially for the structural design, the fabrication and the construction. Without the proper handling and understanding of the involved geometry no project would have been realized in such a high quality. We will present in detail the project called “Splitterwerk” implemented in summer term 2016.

This paper presents a geometric, constructive and structural analysis, of the Encarnación church dome in Montefrío, Granada (Spain). It’s a hemispherical dome, built of stone in the 18th century; the result of the confluence of three trends at that time: Bourbon centralism, illustrated academicism and architectural neoclassicism. Its diameter is approximately 30 m, it is considered to be a replica of the Pantheon in Rome, having been the largest stone dome in the world, since the bombing in 1943 of St. Hedwig’s Cathedral dome in Berlin, until the construction in 2008 of the Global Vipassana Pagoda in India. We present the geometric modelling of the dome, taken from three-dimensional scanning applied to architectural research. We also include an analysis of the mechanical behaviour of the dome is made, analytics and graphically according hypothesis of Rankine-Schwedler, including detailed graphical diagrams.

In the field of lampshade design, paper folding method has been highly utilized as the non-flat texture by paper folding method can generate beautiful luminance distribution. Especially, if the non-flat texture is composed of curved surface units, luminance distribution in the units is continuous and visually soft. And the method combining non-flat pattern and geometrical transmittance pattern has been already proposed to overlap luminance distribution caused by non-flat texture and that by transmittance pattern. In this paper, plane tessellations are introduced to expand diversity of lampshade design. Two methods were proposed with single tessellation and multiple tessellations. With single tessellation method, a tessellation was used for both paper folding and geometrical transmittance pattern. With multiple tessellation method, multiple tessellations were used for paper folding and geometrical transmittance pattern respectively. To verify the effect of the combination, lampshades with non-flat texture and geometrical transmittance pattern were manufactured and brightness distributions of them were measured.

The organic principles conceptualized and written by Frank Lloyd Wright in his books reveals strategies and geometry underlying in his designs along his career. There is no specific study about the geometry of the ramps adopted by the architect in a few designs in different themes, and mostly how this circulation element is linked with his organic principles. The scope of this paper is to disclose the values of the ramped surfaces, as well how its geometry is intimately connected with the principles of continuity, simplicity, plasticity, integrity, and grammar. The focus of this paper is to reveal the geometry of fifteen designs by diagrams, in order to indicate a unique and integrated design, where the ramps present themselves inseparable from the building as a whole, mainly by means of curvilinear forms.

Sun shading is one of the possibilities to rise energy efficiency of buildings. Green structures that combine structures of buildings with living plants are biotechnical elements of buildings. They can rise energy efficiency of buildings. One of the useful properties of the green constructions is sun shading possibilities especially for terrace greening. The most radical method is using the vertical façade greening, which can fully shade glazing. The main problem is that the glazing cannot perform its main function—looking through it. The terrace greening can provide the most natural shading as in a park. Impossibility of full shading gives the necessary insolation of rooms in the most of cases. In this work, there are recommendations for design of the constructions for the Sun shading. There are recommendations for plants assortment, algorithms for analyzing of the Sun position for this purpose and an example for building the figure around glazing for filling it by the plants.

Planetariums are the equipment and the facilities which reflect light who rose from a projection machine in an installed curved surface screen inside the domed ceiling. This can reproduce a star and a stellar movement. The optics system planetarium was put by the beginning in the center of the dome. A recent planetarium can be indicated using more than one digital projector. A digital projector can also project something besides the star onto a dome. It’s possible to project a picture of a PC at this planetarium. The planetarium in Toyama Science Museum held the concerts. And it held the screening party of fulldome contents contests since 2016. But it’s difficult a work will imagine the curved surface, and that’s to make the full dome picture projected onto a planetarium at a plane of a PC. We take a picture of the one which was drawn in canvas in inside the bowl and full dome which says by a fish-eye lens and project onto a dome in a planetarium by this research. We led that full dome picture can be made easily. This paper carries a result of the workshop for children.

The representation of geometric concepts of three-dimensional space is a well-identified predicament that can undermine the understanding of geometry in particular, and mathematics, in general. Branco Grünbaum mentioned that no method of presentation is satisfactory for much more than the simplest situations and expressed the hope “that computer-based modes of presentation will alleviate this difficulty in the near future” [1]. Aiming to address specific concepts of polyhedral geometry, we’ve been exploring a 3D modelling software and its graphical algorithm editor as digital tools to illustrate certain concepts through accurate graphical descriptions that are dynamic and interactive and imply the knowledge of several geometric operations. Among the several possibilities that could illustrate the software potential, we have chosen the concepts of expansion and contraction of polytopes conceived by the Irish mathematician Alicia Boole Stott in 1910 [2], in our opinion, one of the most visually interesting for a dynamic description. For the sake of concision, we will restrict our presentation to two- and three-dimensional polytopes and illustrate the possibilities of dynamically interact with virtual models to visualize, in real-time, the expansion and contraction of regular polygons and uniform convex polyhedra. The purpose of this research is thus to graphically clarify Stott’s methods through a dynamic approach made possible with contemporary digital tools and demonstrate how this kind of analysis may simplify further researches on the subject and enhance the didactics of these concepts in particular and, more generally, of polyhedral geometry.

The current contribute focuses on parametric digital modelling applied to Curioni’s studies in order to in depth analyze the relationships between vaulted surfaces and Geometry. Specifically, the research focuses on the investigation, interpretation and parametric modelling of the intersection between homogeneous surface classes for the definition of punctual elements of compound vaults (groins). The aim of the work is principally analytical and lays its foundations on investigations and studies on vaulted systems present in treatises and manuals. In fact, starting from the study of the sources it was possible to extract from the different cases conceptual geometric diagrams that can be stressed by the parametric modeling. This is done to represent the main spatial quality of architecture under varying parameters. The model is thus aimed at reproducing the theoretical models underlying design concepts to enable rapid and efficient exploration of the different geometric configurations. Therefore, a simple parametric model should represent the spatial qualities of the various architectures while highlighting similarities and differences.

In this paper, the authors present a brief description of the ideas of scholars and artists, who sought to systematize the laws of Perspective, and compare them with the breakthroughs made in recent times. In this comparison, it is given special attention to the compositions that invite those who attend their exhibitions not to merely watch scenarios but also interact with them and experience an anamorphic immersion in a kind of a magical world. The article includes several photos, which were personally taken in places where the positioning of planes allows the observers to complete an image, provided it is observed in accordance with a certain point of view. Under certain circumstances, the visitors can even be included into the scenographic set, acting as extra characters in the 3D simulation. The authors highlight the creativity some street artists employed in designing their murals, and analyze the procedures taken and described by them to display their works to an audience composed of visual effects addicts. Some excerpts of interviews, when the artists provide information on their working methods and show their enthusiasm for the several possibilities of creating new plastic scenes, are a vivid example of the integration between Geometry and Art.

Currently there are more than 154 planetariums in Japan. These are the members of the Japan Planetarium Association (JPA). T A planetarium in japan has an image showing the contents related to the universe. According to the update data of the equipment for screening the planetarium for the past three years, digitization of screening equipment of the Japanese planetarium is in progress. It is introducing the digital planetarium system at Takasaki Municipal Juvenile Science Museum as an example. In addition, we introduced the digital planetarium “Stella Dome” developed by Astro Arts Co., Ltd. at Yokohama Children’s Science Center as a result of screening of animated images. The animated images currently being shown are Pokemon Sun & Moon and Space Brothers, Doraemon, etc. In this way, animation works are screened using planetarium. Therefore, the planetarium not only displays images related to the universe. Therefore, we propose a kaleidoscope type video content that creates patterns by projecting one image like a mirror as new contents using planetarium.

This study attempts to develop an agent-based model to simulate aircraft movement considering an air traffic control system and to provide a simulation method for designing an optimum flight schedule. In this paper, we examined interactive visualization methods to compare simulation results with actual flight data, analyze the causes of air traffic congestion, and find clues to optimize the operation plan. Air traffic congestion is a complex phenomenon in which the macro behavior depends on the interaction of individual aircraft. In order to simulate this behavior, we used a cell automaton (CA) model, which was said to be capable of reproducing such phenomena with simple local rule settings. We developed two types of programs to visualize both the simulation results and the actual flight data. The first is a fly-through program to verify aircraft movements in a three-dimensional space from any viewpoint. This program enables instantaneous search and playback of time-series trajectory data. The second is a flight route analysis program to draw two-dimensional tracks based on flight data as well as display additional information, including time, distance, waypoint, and airport. As a result, we herein propose a three-dimensional visualization method to facilitate the intuitive understanding of macro air traffic phenomena by 3D-CG animation of aircraft movement at a high frame rate and provide a visualization system for comparing and analyzing flight routes by graphically displaying numerical data such as flight distance and current position of aircraft.

Standardization and modularization are common means of simplification and economization of engineering structures. Extremely modular systems (EMS) are comprised of very few (ideally just one) types of modules and allow for creation of structurally sound free-form constructions. Truss-Z (TZ) is the EMS considered in this paper. It is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and their combination). A family of shapes including: isosceles quadrilaterals (concave and convex), regular and irregular kites and darts, isosceles triangles and trapezoids has been considered for the planar projection of Truss-Z modules (TZMs). It has been shown that isosceles triangles and trapezoids suit best TZ. The universality of TZM has been assessed by measurement of the regularity of distribution reachable points by given TZ built with several such TZMs. It has been shown that the vertex angle (θ) of 32.5° gives the most regularly distributed, thus universal TZ.

Recently, intensive emergence and spreading of 3D printing can be observed. Educational institutions become owners of desktop 3D printers implying the need of rethinking what to teach at schools at different levels. Since 3D printing needs a 3D model too, users have to refresh or acquire some mathematical knowledge to become successful modelers. Especially geometric and spatial skills are of high importance when designing a new model, while it provides also a brilliant motivation why to study theory and concepts, and why to understand more precisely the different elements of geometry. Nevertheless, users have to get to know new concepts (such as rafts, supports) and properties (such as watertight) as well, which appropriate usage is essential to be able to print the model correctly. Parallely, they will experience, that some traditional geometric concepts, terms may be interpreted in a more flexible way in the context of the currently used 3D modeling software. The objective of the paper is to investigate how the terms mentioned in the title interact with each other and to demonstrate it by examples. Paying attention to these altered, reinterpreted concepts is crucial in order that we could avoid misunderstandings in math class.

The paper presents the technological aspects and a workflow of creation of the smallest Nativity Scene in the world. The “Nano Holy Family” sculpture took 3 months to produce. The team consisted of students and professors from two universities, business companies and governmental institutions. The sculpture was created in the following steps: scanning, model preparation and nano-fabrication. The scanning of all 15 figures of the holy family was performed using “Sense” V2 3D scanner. After the scanning all the figures were specified and corrected using Blender and Netfabb software. Finally, femtosecond laser based nano-3D printing took place, materializing the Nativity Scene in micro-scale. Because of unmatched precision of applied technology, the Baby Jesus is less than 23 µm high—it is smaller than an average human cell. The presented results show great synergy between 3D scanning and 3D laser nanolithography allowing to down-size to the micro- and nano-scale basically any structure that can be 3D scanned. The project was a result and great example of successful collaboration between business and academia bringing together the knowledge and expertise from academia and technologies from the industry.

We consider the reverse engineering problem to construct a $$G^1$$ continuous interpolant to a triangulated set of 3D points and corresponding normals by fitting a composite surface consisting of rational triangular Bézier patches by using the so–called rational blend technique. The proposed method gives a solution depending on free shape parameters which are fixed by minimizing different functionals linked to suitable surface metrics. It is illustrated by significant application examples.

This paper focuses on the generation of complex geometrical models with solid elements in historical masonry buildings, suitable for structural simulations. The complexity of the system is addressed by dividing it into parts following the typical observed hierarchy, e.g. (a) pier, (b) walls, (c) nodal zones, (d) vaults, etc. Automatic procedures are developed to model the most complex parts of the structural system such as the masonry vaults or the nodal zones. The result is to generate the solid geometry of the structure using a parametric model, with the advantage of significant reduction of the modelling time and better meshing for numerical simulation purpose. The developed models according to the proposed automatic reconstruction procedure can be used for the creation of the geometric model as well as the structural model.

Selective laser melting (SLM) is a complex process involving solid-liquid conversion of metals, heat conduction, thermal radiation and other processes. The warping deformation of the forming parts in the process of SLM is usually the main reason affecting the forming precision of the parts and restricting the development of SLM technology. It is necessary to be probed into the rules of SLM forming process. The thin-walled parts are especially prone to warping deformation because of the fast heating, heat dissipation and the uneven distribution of the temperature field. Therefore, in this paper, the transient finite element analysis of temperature field, stress field and warping deformation of simple thin-walled parts are carried out based on APDL language in ANSYS software. The relationship of temperature gradient, internal stress warping deformation is investigated firstly, Then the rules of influencing the forming accuracy of the parts is analyzed from the whole molding process. Finally, through the analysis of several different scanning molding methods, further studied the influence of the scanning path on the forming precision of the parts. And explored the method to improve the forming precision of the parts by optimizing the scanning path.

Because the double curvature arch dam has the characteristics of distributing the stress for existing loads, it is more and more applied to water conservancy projects. The variable diameter involute double arch dam is an arch dam formed by the arch axis following the path of involute, a new function derivation process is proposed for the variable diameter involute double curvature arch dam, and the arch ring equation is obtained, and c++ programming is used to realize the automatic calculation of the computer, the 3D solid model of variable diameter involute double curvature arch dam is drawn. On this basis, a finite element analysis model of variable diameter involute double curvature arch dam is established, and the analysis results are obtained. For the application of this new arch dam in water conservancy projects, it provides theoretical reference for mathematics and mechanics.

In a current research project in cooperation with the Fraunhofer Institute for Ceramic Technologies and Systems IKTS a complex structure was created which spreads two liquids in such a way that they can blend especially homogeneously. To realize this application, a Peano curve was used Four different iteration steps were arranged in which one curve was placed above the other and a NURBS-based surface was put above the curves. This structure may serve as a mixer for two fluids or as a basis for the construction of heat exchangers. Because a space-filling curve maps a set of points uniformly and constant in a coherent series, it separates two fluids perfectly while the needed surface area for heat exchange is maximized. The main purpose of this study is to analyze and examine particularly simple mechanisms to construct alternative curves with a similar mapping structure. This research also aims to develop a curve generator based on the so-called Lindenmayer system. Through combining several basic curve-motifs, a multitude of curves with simple parameters for evaluation and optimization algorithms will be provided. This paper presents the possibilities introducing only 2 × 2 and 3 × 3 grids. In fact, the presented algorithm already produces about 15,000 different structures and therefore sets a solid foundation for further investigations.

The subject area of geometric-graphic education in the higher technical education is described. Descriptive geometry is the theory of geometric shaping. Engineering graphic—the creation of technical documentation. It is realized by means of computer graphics. Thus, the modern academic discipline “Computer graphics” can unite these areas. Geometric modeling is considered. The requirement for an electronic geometric model of the detail is singled out: the detail model must be editable—retain its geometric integrity with changes in the values of size constraints, i.e. should be predictably correctly rebuilt when making changes to the values of size dependencies. The stages of construction of an electronic geometric model of the detail are shown. The strategy of constructing electronic geometric models of the detail is presented. The selection of electronic geometric modeling as the foundation of geometric-graphic education provides constructive use of the developing possibilities of computer graphics. The content of the educational discipline “Computer Graphics” is presented. Lecture topics are named. The content of practical exercises is described. Video lessons are listed. Informational graphic education provides the following basic competencies for the students: to know and apply the theory of geometric modeling to create electronic geometric forms of objects of technology and technology and be able to create electronic technical and technological documentation using modern graphic technologies.

The legged robot has strong structural flexibility and environmental adaptability, and can walk reliably under unstructured terrain such as mountains and hills. It has various uses and has become a research hotspot in the field of intelligent robots in recent years. In this paper, a quadruped robot is taken as the platform, and the gait planning of quadruped robot and the optimization method of its foot trajectory are studied: 1. the optimization design based on gait parameters. The optimization of step sequence focusing on static gait stability of quadruped robot problem, the optimal step sequence based on the stability margin of the support polygon is studied. 2. The optimization design based on foot trajectory. The influence of quadruped robot’s motion performance by changing the local geometric characteristics of foot trajectory was studied. 3. The structure design and the idea of the physical prototype of the quadruped bio-robot are expounded systematically in the paper. Using the optimized Bezier curve as the robot foot trajectory, the validity of the optimal design of the foot trajectory was reliably verified.

This paper presents a new approach to maximum likelihood fitting of lines in images. Standard approaches such as the Hough Transform are heuristic and dogged by the subtleties of quantization error. As an alternative, we take an analytic approach to the Hough Transform coupled with principles of robust maximum likelihood line fitting. We derive two line-parameter likelihood functions based respectively on the heteroscedastic Gaussian distribution and the symmetric bivariate Cauchy distribution. For these functions we establish a Nyquist rate and threshold values such that all local maxima (lines containing a minimum number of points) are found; the analytic form of the likelihood function is used to obtain precise estimates of the line parameters. Finally we obtain analytically the first order covariance of the estimated line parameters, and hence a confidence envelope about the fitted line. Contrary to popular belief this is not obtained by analyzing the shape of peaks in the Hough space. The motivation for this paper is to establish a rigorous framework for finding curves in images in a maximum likelihood sense; only armed this foundation can the more difficult problems in pattern recognition be addressed in a rigorous manner.

This paper discusses the issues of orthogonal distance geometric fitting, the registration of multiple data sets, and identification based on geometric features for very large data sets of spatial measurement data obtained, for example, from a 3D scanner. The data of interest is obtained from an industrial application, namely, from inside a tunnel as it is being bored and reinforced with tiling. The task at hand is to identify each of the tiles in the scan, and to determine whether their position and geometry satisfy given tolerances. The paper describes a chain of processing whereby aspects of approximation theory, image processing, differential geometry, and pattern recognition are applied. The processing steps are determined as tradeoffs between the desired accuracy of the computation and its computational load.

The cavitation phenomenon in water-hydraulic transparent valve was studied regarding the morphology of bubbles in the process of cavitation in this paper. Firstly, the setup with a multi-angle plane mirror imaging system was built, and the experimental image data of the water-hydraulic transparent valve was collected and stored by a high-speed camera and an Industrial Personal Computer (IPC). Then, a bubble in the process of cavitation was selected and the 3-D reconstruction of this bubble was rendered by multi-mirrors about the obscured effect of spool. Finally, based on the case library of artificial intelligence CBR, some criteria had been used to co-determine bubble cavitation effect in terms of the critical values S, N and R of the bubble cluster shape, the number of bubbles, and the average size of the bubbles, respectively. When one parameter is larger than its critical value, the phenomenon of lighter cavitation appears. Meanwhile, when two or more parameters are larger than their critical values, serious cavitation is possible. In this study, the experimental results validated the feasibility of those criteria.

To solve the problem of the large computation and low recognition rate which caused by the K-Nearest Neighbor (KNN) algorithm, a new approach for facial expression recognition based on weighted K-Nearest Neighbor and Random Forest (RF) is presented in this paper. First of all, the features of the static facial expression image are extracted by the Supervised Descent Method (SDM), then calculate the average distance between samples and use it to divide test samples, select different classifier for different test samples base on the characteristic of weighted KNN and RF. Finally, the result of experiment on JAFFE database show that the proposed algorithm can not only achieve better recognition rate, but also simplify the computation complexity.

Direction is an important factor affecting the impression and quality of video contents. Therefore, the director must carefully decide the direction scheme. Especially unless the character’s emotions are directed effectively, viewers cannot empathize. Therefore, the director must carefully design the direction based on the theme and intention. Among them, lighting and composition are important factors directly affecting visual appearance. Therefore, careful design of lighting and composition is necessary. However, the direction depends on the experience and sense of the director. In other words, it is difficult to reuse the direction method and to preliminarily confirm the effect of the direction. Therefore, in this research, we focused on anger even in the character’s emotions. Furthermore, support to design of the composition and lighting for directing angry characters. In this research, we investigated and analyzed human anger. There are various causes and behaviors involved in anger. The impression to angry characters of viewer is varies depending on the causes of anger. Therefore, we classified each shots that angry character appears. This classification is based on the cause of anger. Furthermore, we analyzed lighting and composition of each shot. Based on these analysis results, we developed data library. In addition, we developed a template that can reproduce the lighting and composition of the analyzed shot with 3DCG. With this template, users can apply the lighting and composition of analyzed shots to arbitrary character models. It is possible to more effectively design the directing for angry character by using the proposed system.

In this paper, we propose a new way to generate videos via recurrent convolutional generative adversarial networks (CRGAN). The video tasks involving spatio-temporal series are more difficult than image tasks. In order to deal with spatio-temporal series tasks, we use a method that combines convolutional neural networks (CNN), which are used to deal with spatio relationships of videos, with Long Short Term Memory (LSTM), which is a variant of recurrent neural networks and used to deal with temporal relationships of videos, called convolutional recurrent neural networks (CRNN) to process the video inputs.Generative adversarial networks (GAN) is a method of unsupervised learning and has attained great improvements in image generation. In our paper, we combine CRNN with GAN and use unsupervised learning to generate videos. In the end, we will present some videos generated by our methods.

In order to eliminate the infertile, weak and dead embryo eggs, which would pollute the normal embryo eggs, the activity detection of embryos need to be carried out before vaccination and harvest of influenza vaccine. Light method is widely used to detect the thickness and lines of blood vessels of chicken embryo to determine the embryo activity in the detection of vaccine strain activity. However, long time light detection is labor intensive, inefficient and easy to cause visual fatigue, which would lead to erroneous judgement of embryo eggs, and long time leaving the incubator will affects the development of chicken embryos. Given the disadvantages of high labor intensity, low efficiency and poor accuracy in the biological vaccine strains activity detection by artificial lighting, a nondestructive detection system of bionic embryo egg based on visual sense was designed. Meanwhile, a new adaptive threshold image processing method based on the minimum class exponential variance is proposed to solve the problem of extracting blood vessels from egg embryo which is affected by different gray level in egg embryo image and low quality of egg shell. The binary pattern of active egg embryo blood vessels were constructed accurately by the edge detection and mathematical morphology processing of the de-noised egg embryo images, the egg embryo activity is determined by calculating the binary area percent and area circumference of egg embryo blood vessels. Through the collection of a large number of active egg embryo images and the analysis of blood texture structure by graphic construction method, the model database of active egg embryo images are constructed to provide a criterion for the rapid determination of egg embryo activity. Results show that this system can detect an embryo egg in 0.039 s and the accuracy rate is 100%, which can meet the requirement of inactivated vaccine and freeze-dried vaccine production. Extraction of vessel texture from egg embryo.

In order to improve the design and manufacturing efficiency of propellers, a dedicated CAD/CAM system for the whirling process of propeller blades is proposed. The main functions of the proposed system include parametric modeling of propeller blades and tool path solution for the whirling process of the blade. The former takes advantage of Creo to construct propeller’s 3D model by means of parametric modeling of the original design data; the latter is aimed to help manufacture the propeller blades using whirling process which is primarily used in producing threaded parts.

In the case of less interference, traditional aircraft target recognition algorithms can work well. However, there are a large number of interfering factors in the remote sensing images actually. At this time, traditional algorithms fail because of low recognition accuracy. Aiming at the shortcomings of traditional methods, this research has proposed a new kind of aircraft target recognition algorithm based on saliency images and invariant moments. The algorithm first uses Itti algorithm to extract salient targets after pretreatment, then uses the 8 neighborhood searching method to find the connected regions in binary images for determining the numbers and location of the candidate targets. Finally, identify the candidate targets by using the combined moments based on affine invariant moments and Pseudo-Zernike moments. The experiment results show that this algorithm has high detection accuracy, less time spent, low rate of false alarm, and it is robust to noise, background and scale transformation.

In consideration of the complex operation scenes such as disaster site and field, the detecting robot must be very adaptable to different environments, such as land and sky, which means a high requirement for the configuration design is very necessary. This paper presents a small air-land amphibious detecting robot that fuses the ground robot and flying robot function. The common ground robots are wheeled robot, crawler robot, foot robot and so on. In comparison, foot robot is more suitable for complex unstructured environments, and the quadruped robot is considered the most promising robot insides. In contrast, the flying robots are often used in the form of the fixed wing robot, multi-propeller rotor, flapping wing robot, helicopter robot and so on. Take the advantage such as strong controllability, flexible movement, and vertical take-off and landing into account, the multi-propeller rotor is a low cost, simple and effective solution, especially quad-rotor aircraft. So this paper proposes the configuration that combining quadruped robot and quad-rotor aircraft. This paper presents a configuration design that combines the quadruped robot and quad-rotor aircraft function together, in order to make this robot has the flexibility of the quad-rotor aircraft and the ground adaptability of the quadruped robot.

Our goal is to create artificial beauty by generating new plane figures—curves not known in Geometry. The paper deals with an original mechanism that generates curves featuring special aesthetic properties. The mechanism synthesis was achieved starting from relations known from Trigonometry for multiple arcs. The angles considered for the aforementioned arcs are represented by the angles of the leading elements, correlated through a coefficient n. The mechanism has two leading elements and two dyads of type RPP, rotation-translation-translation. In the extended paper the cinematic schema of the mechanism is provided. Its structure is analyzed, the associated equations are introduced along with the obtained plots (many curves with special aesthetic properties). Comments are made with respect to the influence of the coefficient n used to correlate the angles of the leading elements over the shapes of the generated curves and over the number of close contours. The obtained curves are analyzed for both possible distinct cases: when both leading elements are rotating clockwise, respectively in opposite senses. The continuity of these curves is studied as well, close or open curves being obtained. Some mathematical properties of the curves generated by the above mechanism are studied (the curvature and the curvature radius in a current point of the curve, the equation of the tangent and the equation of the normal to the curve in a current point and the symmetries of the curve with respect to the coordinate axes (Ox axis and Oy axis) and with respect to the origin O).

The design of a tensile structure differs from the one used in conventional structural design in that it is impossible to predict the tensile structure form. This paper describes a special 3D Frame-Grid template for efficient form-finding of the tensile structure. The basis for the template is a Frame object consisting of a set of spatial edges, connected with each other in vertices. The Frame edges and nodes correspond to fabric structure singularities and to boundary constraints. The grid is hung on the Frame object and is subject to optimal form-finding by the Stretched Grid Method (SGM) as close to the minimum surface as possible. Moreover, the problem may occur when designing awnings with a “narrow neck.” Taking into account this singularity, we provide a special adaptation tool based on a non-linear function for each weight ratio of the Grid edge separately. The final structure surface inherits geometric properties from the Frame object. Therefore, the Frame-Grid template makes it possible to redefine the surface form automatically, modifying only the Frame structure. However, the numerical problem solution leads to the fact that the final surface is represented by an arbitrary polyhedron. This may cause the appearance of surface wrinkles or folders at some narrow surface regions. To avoid this, we developed a special corrective criterion. In many cases, a structure’s integrity, stability and safety may be based on a “pre-stressing” process. The paper describes the way to orthotropic non-dimensional pre-stressing taking into consideration the twofold difference of rigidity between warp and weft directions.

Orthographic drawings still have an important role in the design and manufacture workflow. An important task for the designer is to determine the most suitable collection of views to represent a solid. Where complex artefacts are considered, and/or inexperienced users perform this task determining the possibility pf a set of views in which there exists ambiguity increases. To begin to address this issue, this paper outlines a method to recognise simple cases of indeterminate solid models, considering underrepresentation by deficiency and redundancy by superposition. The method employs multipartite graph and cellular modelling to deal with each case, and it has the potential to be fully automated within a CAD environment. Entities which are underdefined require more information to be fully defined can be identified.

Editable and convenient geometric models are used for solid representation in engineering environment. As the industry has evolved, CAD systems changed to accommodate the need for a faster pacing design timing. Models became refined and exchangeable so that any change can be seamlessly propagated through the model and connected assemblies. Despite the fact that most of the design and development takes place on three-dimensional models, todays industries still store and rely on legacy drawings. For the last 30 years’ multiple solution methods have been formulated for reconstruction of 3D models from orthographic projections. However, these models do not carry design intent making them harder to reintroduce them efficiently in the design workflow. This paper outlines in detail a method for “reconstruction-recomposition”, reconstructing solid as individual features and composing them within the same solid model. The method is tested on case studies evaluating challenges of scalability and application to industrial cases.

With the wide spread use of 3D-CAD in industrial fields, some people say that traditional descriptive geometry is no longer any use. In fact, typical descriptive geometry problems such as finding the true length of a straight line and the intersection lines between two solid objects can be solved much more precisely and much more quickly with the use of 3D-CAD than with hand drawings based upon traditional descriptive geometry. Is the traditional descriptive geometry really no longer any practical use? In order to get some insight into this question, we solve some applied geometric design problems with the use of 3D-CAD, and compare the solution processes with those in traditional descriptive geometry. The results of comparison show the followings: (1) Solution strategies in 3D-CAD are basically similar to those in traditional descriptive geometry. Even in 3D-CAD solutions, the use of graphics representations (i.e., 2-dimensional representations) such as projection from a specified direction, development and sectioning are quite useful. (2) It is, however, not necessary to use traditional rules and compasses to get such graphics representations. Projection function and sectioning function in 3D-CAD are useful in getting graphic representations. (3) Much easier solution strategies are sometimes available in 3D-CAD by applying rich 3D-CAD geometric processing functions such as assembly function. (4) Knowledge on spatial geometry just behind traditional descriptive geometry is, needless to say, still important in 3D-CAD solutions.

Based on the BIM concept, the Revit API class library is used for secondary development on the Revit platform, combining with the “Design Guidelines for Highway Cable-stayed Bridges” (JTG D65-01-2007), according to the parametric design problem of cable-stayed bridges. According to the bridge’s component type, we can construct the parametrical model in the Revit view to generate the structural component model of each part of the cable-stayed bridge. This study provides a new method for the three-dimensional visualization design of cable-stayed bridges.

3D CAD is a tool for designers to transform ideas into a shape and examine and finalize such ideas. If techniques related to 3D CAD are effectively used, time and confusion can be reduced and an effective tool for representing design information can be established. Therefore, to establish a new concept of drawings, we should examine the effective use of 3D annotated models. In this paper, (1) fundamental knowledge of machinery is generally examined to design machines using 3D CAD. (2) Improvement in the skills of machine designers is also examined by considering the shape modeling technique using 3D CAD (design = shape determination = ambiguity reduction and shape contriving). (3) The significance of 3D annotated models and the training method for beginners in mechanical design are explained. (4) The actual design process is examined and analyzed, and an example of a practical training method is introduced. To effectively utilize 3D CAD, users must understand its characteristics and fully utilize its functions. Satisfactory learning effects were obtained through design training using 3D annotated models for beginners in mechanical design, who received courses on fundamental knowledge of mechanical design and performed practical design assignments (geometric dimensioning and tolerancing) simultaneously.

This paper presents the results of the educational activity carried out within the Fashion Design Course concerning the folding surfaces, and their applications at different scales. The goal of this study is to put the students in front of a geometric process that from the plane leads to the three-dimensional spatiality of the object, according to a construction opposite to a traditional one. This consideration shows to students the different possibilities that geometry offers both in the design process and in the project presentation. The methodologic approach adopted confirms the well-known importance today of the drawing as medium of critic interpretation not only about the complex surfaces and their three-dimensional organization but also the conceptual process that has generated them. The educational activity articulated in consequential phases that puts a student in front of a geometric process that from the plane leads to the three-dimensional spatiality of the object, according to increasing difficulty levels. This study will continue extending the results obtained on the analogic folds to the possible developments in the digital environment, in order to allow students to manage with a critical and scientific awareness the drawing of the fashion product also through virtual simulation.

This contribution reports on an ongoing teaching experiment based on Oliver Byrne’s edition of Euclid’s Elements in colors. Byrne’s idea was to present Euclid’s statements, constructions and even proofs with a simple and (in a certain sense) rigorous use of colors, as a way for synthesizing more explicit verbal descriptions and argumentations. In our experiment, developed in two classes of grade 10 students, Byrne’s idea is combined with the use of a free dynamic geometry environment, Geogebra. Interactive Geogebra applets in Byrne’s style are created both by the teachers and by the students and used as a tool for exploration of properties and mathematical discussions; they are also used as a tool for making explicit students’ understanding and learning of Euclidean geometry.

This contribution is intended to show that the events of geometrical drawing in Italian schools may be a good case study for the interplay of institutional and epistemological instances, and their impact on the actual implemented curriculum in classrooms. First, we retrace the institutional development of official curricula- focusing on three main turnpoints: the birth of Italian unitary school (seventh decade of XIX century), with the work of distinguished geometers like Luigi Cremona, Francesco Brioschi and others; the Gentile reform (third decade of the XX century); the new 2009 and 2012 curricula. Second, we examine some important epistemological debates on the nature of geometry and the role of drawing, focusing on two moments: the discussion carried on by Giovanni Vailati and Federigo Enriques at the beginning of the XX century, and the debates following the explosion of “modern maths” in the second half of the XX century.

The main task of universities is the preparation of qualified graduates who have modern competencies and can compete in the labor market of engineers. The program of educational maintenance and support of activity of gifted students is submitted. Its educational installation and results of the program in mastering participants of various competences is opened. The main indicators of efficiency of educational process of maintenance which optimum entry of the student into innovative activity allows are defined. The contents of the program with structure and the thematic plan are provided. Stages of the main actions for implementation of the program in relation to conditions of preparation of students for participation in the Olympiad in graphic information technology are covered. The article shows examples of the models who students were created during the participation in various Olympiads on 3D-modeling and prototyping. Work is directed on further search of effective methodical systems of training of gifted students to computer graphics.

During the Fall 2016 and Fall 2017 semesters, a geometric dimensioning and tolerancing (GD&T) course was offered at Illinois State University. The purpose of the course was to introduce students to basic concepts of GD&T and then allow students to complete practical exercises and laboratories to apply the concepts. This paper outlines the main topics and structure of the course, describes laboratory activities and how they tie GD&T concepts to solid modeling concepts, summarizes some of the assessment data gathered during the Fall 2016 and 2017 semesters, and analyzes student performance on concepts presented during both semesters. Preliminary results indicate that students appear to perform well on concepts that require only the recall of information (e.g., symbol identification, placing datum feature symbols on surfaces, etc.). Students did not perform as well on the application of concepts (e.g., recognizing the location of a datum reference frame origin, calculating the virtual size of a hole, correctly applying specified limit dimensions, etc.).

Undergraduate programs in Engineering, Architecture, and Design offer courses on Descriptive Geometry and Technical Drawing at early stages, to provide students with basic knowledge to deal with subjects related to representation throughout their careers. However, first and second-year students face some problems, as they have small (or none) experience with orthographic views and need to learn this form of communication at the same time they are learning it. A way to diminish the level of abstraction of those courses is to engage the students in meaningful activities and hands-on experiences, providing them with empirical-concrete resources, so they can manipulate and analyse tangible objects, instead of devising abstract elements. This paper proposes a way to ease the transition from 3D objects to 2D views, leveraging the spatial abilities and reasoning of the students, using constructive blocks through a design-based learning approach. The blocks are provided at the beginning of the course and serve as support for the classroom activities.

In this paper it is discussed the MATHEGRAPHIC workshop, aimed at the learning of Math, Geometry and Graphics by an interdisciplinary and dialogic approach in which the knowledge gained from each discipline becomes a useful support for the learning of the others. This approach is aimed to foster connections among the teaching and the learning of architecture and art history, graphic survey, handmade and digital drawing, geometry and mathematical analysis. Starting from the knowledge of the architectural cultural heritage of the early decades of the twentieth century and from the graphic representation of the decorative motifs that characterized the Art Nouveau and Art Déco styles, it has been proposed a program of study of the forms aimed at the graphic, analytic and algebraic representation of the structures characterizing the decorative motif, as well as at the use of this knowledge in the field of architecture and design.

To make the geometrical cognitive process more interactive, we produced teaching aids (tangible models, graphic tablets) that help students in visualizing their geometrical-analytical investigations of the architectural artifacts and enhance their spatial prefiguration and critical form-reading skills, three-dimensional thinking and geometrical reading of shapes. Then, we looked for a medium suitable to create simple three-dimensional models, not only observable, like virtual models, not only tangible, like physical models proposed in the design studios, but also dynamic, using multiple media and languages in the same training message. As an example, we present here an interdisciplinary lesson between Calculus and Architectural Drawing and Survey Laboratory about developable surfaces, experimented on first year students of the bachelor program in Architecture. The lesson is based on the use of a graphic tablet and some origami inspired models: it summarizes the geometric description of a pyramid and a cloister vault of equal height and equal orthographic projection on the horizontal plane. We saw that tackling the same topic in both teaching contexts is not a useless overlap, but a stimulus to compare different languages and methods. 2D and 3D paper models of artifacts—and of projective reduction from 3D to the plane—aid spatial intuition and the subtle exercise of controlling mental images which replace artifacts, turning 3D configurations into signifying images. Moreover, this experience stimulates reading and evaluation of the drawn geometry (ruled surfaces, projections, developments), increasing critical sense in reading the built environment.

Geometrography, or “the art of geometrical constructions”, was conceived by Émile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions. Along the 20th century, a few authors proposed different approaches and perspectives to the study of geometrography. One one these works was produced by Brazilian geometer Virgilio Athayde Pinheiro in mid 1970s. Unlike Lemoine, that restricted his analysis to the number of operations performed to solve a given geometric problem, Pinheiro chose to explore the theoretical background that supports the exactitude of ruler-and-compass constructions. Moreover, Pinheiro organized a solving-problem method that favors the development of geometric thinking and deductive reasoning. Although this method rests virtually unknown to most Brazilian mathematicians and math teachers, it remains valid to be used even in traditional classes as in dynamic geometry environments. This paper presents an overall view of Pinheiro’s geometrography and a brief analysis of its role as a theoretical reference and as a teaching resource.

Drawing is the language of communication between engineers. Using of the language requires learning of the vocabulary, rules of grammar and syntax. The rules of Polish grammar are different from the rules of English, German, Lithuanian or Slovak. The vocabulary of these languages is also different. Implementation of the international project under the Erasmus + Programme, “Development of Interactive and Animated Drawing Teaching Tools”—DIAD-tools No2017-1-LT01-KA202-035177, which was started at 1st of October 2017 and is realized by partners from Estonia, Latvia, Lithuania, Slovakia and Poland, has become an inspiration to ask the authors themselves—is the constructional drawing an universal, international language? The main goal of the project DIAD-tools is to create interactive tools to support the learning of technical drawing. These tools will be available on the online platform available for university’s students, college’s students, school’s and universities’ teachers from different countries. Developed interactive and animated drawing’s materials should be universal, in order to constitute a genuine teaching aid. Therefore, the question about the universal nature of the constructional drawing used in different countries is so important. The authors compare the adopted standard designations of a constructional drawing in force in partner countries implementing the DIAD-tools project. The comparative analysis carried out will enable the development of a maximum universal illustrative material for learning the principles of constructional drawing. At the same time, it will enable the development of illustrative supplemental materials that will contain information about possible differences in the drawing’s symbols or rules that are used in countries of the project’s partners.

With the rapid development of network and information technology, the textbook is not only limited to the publication of the paper media, but also closely related to the Internet. Traditional teaching materials of cartography began to transform and upgrade to various forms, such as the combination of various new media forms and traditional books, the application of virtual reality VR technology and augmented reality AR technology in the publication of new form textbooks. This paper introduces the concept of augmented reality (AR) and feature technology, the basic paradigm and application mode of augmented reality technology is applied to the analysis of the publication of textbooks; compiling and writing introduces how to make use of the augmented reality technology and teaching resources for new forms of teaching. AR augmented reality technology in the mobile phone APP into the difficult understanding of the graphic graphics into a three-dimensional model, and can be multi angle, zoom, narrow the interactive view. The combination of AR augmented reality technology and cartography teaching materials can bring more 3D three-dimensional experience and enhance readability of textbooks, which not only makes learning easier, but also makes classroom learning more vivid and interesting.

20th century modernity brought us the decoupling of design and design representation as well as a steep decline in the authority of expert knowledge. The wider public is allowed to participate in decisions and, therefore, ought to be enabled to decide in a rather educated fashion. Architects and urban planners are caught up in the middle. They have to convince their audience verbally—prospective customers, tenants, spin doctors and bystanders alike—that their unique design (as visually displayed on the wall) will be ultimately satisfactory not only for the duration of a short-term advertising campaign but also for a long-term project with significant impact on multiple aspects. What we can agree on: The successive mode of persuasive rhetoric and the momentous fascination with graphics at a glance. We ‘buy’ a verbal argument only at the conclusive end of the story while we are subjected to the visual allurement of the first glimpse: You never get a second chance to make a first good impression. I suggest public presentations as calculation of the overwhelming simultaneousness of information that is structured according to the succession of the potential verbal explanation irrespective of the presence of the authors. We show visually what we want to explain verbally. We illustrate explanations rather than display planning. The quest to extract information complexity in public presentations meets the current implementation of increasingly complex Building Information Modeling (BIM) systems.

The article describes the experiment held among junior engineering students of technical college with purpose of developing creative potential and formation of professional engineering culture. The biomimetic approach in training of future engineers based on that way to creating technical devices when the main ideas are adopted from wildlife. Search of the ideas gives student the chance to feel as the engineer-inventor which is very important for generating professional culture at initial courses of higher education institution. The creative component of professional culture of the engineer implies ability to an invention and realization of something new in the equipment or technology. The first- and second-year students were offered to fulfill the following creative task: to study a biological object and to develop mechanical unit similar to this object or to develop a polysurface, to create virtual model in CAD package they are studying and to present their design. This creative task involves cross-disciplinary knowledge in biology, the theory of mechanisms, descriptive geometry, and engineering and computer graphics. The article also gives description of results of a research, how much the performance of creative task promoted the solution of the assigned educational tasks. The pilot experiment has shown that creative works have significantly increased the interest of students in self-reliant obtaining of information—additional in relation to course of engineering graphics. Performance of creative work with application of biomimetic approach, has led to increase in interest in engineering graphics and the involvement into designing, development of creative potential.

Architecture has always relied on mathematics to achieve proportioned aesthetics, geometrical consistency, structural performance and reasonable construction. However, since computational tools have given architects the means to design and build complex spatial concepts that would have been inconceivable even twenty years ago, the discussion on how to integrate computation into the architectural curriculum is still ongoing. Against this background the academic project “Shell Tessellation” focused on the early integration of mathematical strategies regarding geometric description, structural performance, physical properties, and material specification as well as aspects of fabrication to inform the architectural design. The emphasis of the curriculum, developed jointly by the Department of Architecture and the Department of Mathematics, was put on research-based design-strategies that aimed to unfold hidden complexities of rather simple geometric definitions. The paper presents the didactic methodology and discusses three selected case studies that were carried out within this interdisciplinary Master course at the Politecnico di Milano.

We examined the effect of using an interactive digital application that uses a real 3D object as its interface on design education. We have identified and tested various approaches cultivating creativity in 3D modeling but have previously struggled to find an appropriate approach. Following the positive results of a pilot design session, we conducted multiple workshops with university students to see if this approach could be effectively employed in 3D modeling education. We compared the difference in the performance of two groups of students, one group were shown a video of the example interaction while the other group were not. We observed a positive response from the participants with the group who watched the video producing many more ideas than the control group. This result convinced us of the effectiveness of our approach. In this report, we provide the results and observations from the workshops, and discussed the potential of this approach.

Mass open online courses (MOOC) are popular recently. Their advantages are obvious: training at any time, from anywhere in the world, from the best teachers, with the help of quality content. But is it possible to learn practical skills through the MOOC? The express-course “2D + 3D design in AutoCAD” proved that it is possible. However, for this purpose, when developing video lessons, practical exercises and tests, it is necessary to take into account the basic principles of effective learning in distance learning. Students of the course for a short time (6 weeks) master the skills of working with the program, learn basic commands and opportunities. At the 7th week, a contest of creative works performed in AutoCAD is held. The level of these works amazes and motivates the new launches of the course. The fact is that with distance learning there are certain advantages, but disadvantages are inevitable. The article describes the experience and conclusions that will help readers in developing their MOOCs.

For architect engineers it is very important to know geometric surfaces in order to use them in the design of buildings. Architectural objects, other than functional, should also satisfy the aesthetic criteria which is achieved through design. The existence of different software packages for modeling like Rhinoceros, with additional programs (Grasshopper), allows doing the rational design and construction of these architectural objects. All these facts were noticed by the authors of this paper, which was further followed by giving the students of Faculty of Civil Engineering and Architecture in Niš, an elective subject Geometric surfaces in architecture in the school year of 2009/10. The content of this subject includes study of all geometric surfaces in architecture practice. The importance of studying Geometric surfaces for students of architecture was noticed by the Faculty of Engineering and Design, Hosei University in Tokyo, Japan, which resulted with offering this elective subject to the students in the school year of 2017/18. The students of both faculties have learned to recognize geometric surfaces and how to apply them in complex geometric forms with attractive appearance. In this paper, the work on both faculties will be shown as they are different, the results will be compared, similarities and differences of working on two different continents. With proper analysis it is possible to make a model of study for this subject in different educational systems.

Matters connected with arisen problem situation while teaching graphic disciplines are considered in this article. Sharp reduction of academic hours for graphic disciplines study and increased requirements for education quality caused necessity to develop new ways of teaching this discipline. One of the possible approaches to improve the situation is redefining the content and forms of teaching engineering graphics. To determine the qualimetric estimate of students used method for constructing the tree of properties. The qualimetric estimation of a student is offered on the basis of internal factors. Positive and negative factors influencing successful training are investigated. Management of the learning process is achieved by the continuous monitoring of students’ knowledge. For each academic group calculated integral indicator of progress. Identified the most of significant factors among positive and negative ones. Analytical dependencies are determined allowing to manage the educational process.

Geometry at technical faculties requires an interdisciplinary approach to determine learning outcomes. Teaching methods, student workload and grading methodology are based on learning outcomes. We are continuously checking students’ abilities in order to keep improving our teaching by adapting new tasks. In the Bologna process, learning outcomes is one of important quality assurance tools. Spatial conception testing has been conducted at the University of Ljubljana’s Faculty of Architecture (hereinafter: the FA) since 1999 and at the University of Rijeka’s Faculty of Civil Engineering (hereinafter: the CE) since 2016. In order to process data more quickly, we started using Microsoft Excel, and then in the 2016/17 academic year together with Lidija Pletenac from the CE we digitized mental rotation test (MRT) to DMRT followed by mental cutting test (MCT) to DMCT in the 2017/18 academic year. In this article the results of DMRT in academic year 2016/2017 and results of DMRT and DMCT in academic year 2017/2018 on both FA and CE are presented. It turned out that students that scored well on the DMCT did not necessarily score well DMRT, which shows that tests measure different parts of spatial conception. At the end of the year, the differences between students in their scores on the MRT at the FA were smaller than at the beginning. The reason for the improvements are all the courses (e.g. Descriptive Geometry, Free Hand Drawing,…) that improve spatial skills in the first year of study.

Although there are many applications for hospitality education via Virtual Environment (VE) platforms, such as role play, and destination exploring, researchers in the field are not considering their use as a graphic design tool for achieving creativity during hospitality education. In addition, spatial related graphic design, such as exhibition design and hotel room design, is an increasingly challenging task for hospitality students. Hence, this study aims at proposing the implementation of potential creative graphics design courses for creativity of hospitality students by use of VE platform. In order to explore the possibility of exploiting the VE platform to achieve meaningful learning of creativity, an evolving virtual learning environment (VLE) facilitated with features that are convinced to be contributive to the proposed educational purpose is being constructed in the virtual world. This study examines previous studies on virtual worlds to facilitate hospitality education via literature review; constructs 3D replica virtual hotel in VLE with its lobby, café, ball-room, restaurant, multifunctional room, and guest rooms; creates experiments of mechanism of re-al-time interactive and automatic toolkits within VE and course materials for assisting student learning in hospitality, a ‘Real-Virtual’ teaching approach, which is in line with their real-life teaching module of hotel guest room design, and events design and exhibition design. This paper reveals that the VE provides a new podium to stimulate creativity potential of hospitality students for their degree module works through doing graphic aesthetics and experiences for both the creating the works and the user interacting with the works.

The abstract should summarize the contents of the paper in short terms, i.e. 150–250 words. The concept of design understood as a precise artistic genre distinguished from others by difference in instrumentation and results, is very old. It has assumed a clear configuration already at the time of Plinio il Vecchio who says that painting would be born from this first phase of representation. In his thought the drawing corresponded to a form of primitive expression, historically prior to painting and differentiated from it by a greater descriptive poverty, which derives from the use of simpler technical means. Drawing, in the most ancient ages, was not considered an expressive category, but a fact of a “technical” nature, a form of language imposed by the tools available. Only later did design become a fundamental aspect of art and know the concepts allows to face painting, sculpture and architecture. In the course of “Drawing Tools and Techniques” within the Design Laboratory of the degree course in Communication Design the autonomous design is realized with the redesign and reinterpretation, through different graphic techniques, of a work of art. The observation, the study and the redesign of an artistic work, abstract or figurative, is a traditional academic exercise that constitutes an important field of application of the science of representation in general and its geometric foundations in particular. Drawing is not the purpose of art, but it is its primary and essential instrument, it is not a means, but an end to art itself. Because drawing is capable of speaking not only to the eyes, but also to the spirit, to interiority.

In general, characters in the video content has a great influence on the works they play a role in. The creation method in the pre-production still depends on the experience and sensitivity of the creators. For that reason, there is a problem of the communication-gap, and it is always created with the same members to avoid frequent occurrence such as re-take. The current state of video content creation education is often done by educators with experience of production, and it is done with empirical rules and sensitivity of each educator. Therefore, there are a lot of relatively technical education, education to solve production problems is very difficult. The authors have developed various proposal methods for the DREAM method. A literal template is a template that can summarize necessary information at the planning stage and can describe character settings and stories. The collage system is a system that makes it easy to create visual materials even for the creators who cannot draw pictures well. The lighting scrapbook and the camera work scrapbook is a camera work and lighting simulation system for planning the optimum lighting in the directing scheme. In addition to these, the authors have developed a system for the emotional expression, the color scheme and the modeling of characters. These various proposal methods are aimed at solving the communication gap in creation. In this research we report examples of using them as an educational tool for character making.

This paper presents the content of the course Fundamentals of Engineering Animation (FEA). The course FEA deals with manlike character animation through four tasks. Before taking FEA the students have mastered 3D character modeling, mapping, lighting and rendering. Also, they are familiar with rigid body animation, as well as with simple animal animation requiring rigging, like fish or animals with simple skeleton. The above mentioned tasks are increasingly more complex and this paper presents the topics of these tasks, details about them and their sequence as well as the evaluation of students’ work. The students’ project requires creating a 3D character mesh as well as rigging and making controls for two cases: Inverse Kinematik (IK) and Forward Kinematik (FK). The first project task (FPT) represents the creation of a simple movement in a sport with several phases: Hold, Anticipation, Target Pose, Overshoot and Hold again. The second project task (SPT) deals with character walk cycle which should be displayed in minimum five walking steps with some personal characteristics. The last task is Final project (FP) which shows the combined movement of the character in which the animation cycle is connected with linear animation. All movements must be shown as happening in the same sequence without interruptions. The aim of the FEA course is that through the four interrelated tasks the students pass through all basic variations of manlike character animation so that they gain the necessary experience before entering the professional production work.

In this paper, we present a new method to utilize the workshops (WS) interpreting café wall illusions. As an example in which our proposed method worked effectively, we show that in a 3-dimensional (3D) scene, when a perspective projection consisting of a solid object with a staircase-like 3D pattern is present, the projected image has a similar structure to café wall patterns, resembling shadows of vertical pillars cast upon a broken surface. Additionally, we showed that the café wall illusion can be explained by our brain trying to correct perspective projection distortions. To the best of our knowledge, this is the first study that relates the café wall illusion to visual 3D-scene processing. We analyze example items created in past WSs, and show that the basic conditions required to create a new expert idea are fulfilled by the entire group as the idea is presented. Thus, the expert idea emerges from collective knowledge accumulation; it does not emerge suddenly from one expert. This is a clue to clarifying how discussions and knowledge level increases are triggered during WSs.

The contribution presents an educational approach of representation and simulation for higher education of architecture and planning. The focus is on the representation of the quality of the intangible urban issues related to the experience of places, that is multisensory perception. Since the topic is not defined by coded approaches, as happens for instance with geometrical drawing, the authors proceeded with a trial and error process, that is an experimental procedure that involved Master of Science students. The paper presents the topic and briefly compare conventional and non-conventional representation, and presents the experience gained in architectural higher education by showing and commenting some outcomes of the course “Architectural and Urban Simulation” at Politecnico di Milano. The educational process aims at merging sensory urban design approach to the representation of the intangible elements of the urban environment, by conceiving representation as a crucial element for well focusing the subject, from the urban analysis to the final output, i.e. the design project.

According to the request by the Ministry of Education, a small project-based learning program on geometry has been designed to invoke interest on graphic science. This program is performed as a part of “Workshop,” a compulsory course for the first year students of Department of Mechanical Engineering. The program consists of four times of three-hour instructions, and a class has 10–11 groups of four students. The subject of this program is to draw the net of elongated square pyramid that maximize the volume on A4 paper. Based on the last year experience, the program has been revised. It includes preliminary project in the first week so that students get familiar with PBL, know what they should do in the project, and that they can concentrate on the geometrical problem. The temporary result is shown because the first class has only finished the second week. The total result will be shown at the conference.

Descriptive Geometry (DG) is the knowledge base for the design process (Engineering, Architecture, and Design). Despite its importance, in many universities, its teaching has been neglected and often has disappeared as a discipline, and its content has been integrated into more comprehensive courses such as technical drawing and CAD. We believe that the DG teaching-learning process should be improved so that the disciplines of technical drawing and computational drawing tools can be better used in the education of designers. For this reason, we developed the HyperCAL3D, an application that performs all DG processes in multiple projections in a virtual environment. Although it is a software to aiding learning DG, its use depends on the knowledge of DG, because there are no automatic solution tools, the user must know the DG solution processes. Thus, this desktop application has allowed teachers and students to use DG knowledge to solve design problems quickly, directly in a virtual environment. This implementation is a milestone for the teaching of DG, as it allows the solution of complex problems in a few seconds, with high precision and with the understanding of the process being carried out. Such approach is a significant improvement because without the aid of the software the student must use the manual drawing as the only alternative, which is slow and laborious, and hinders the learning process.

The paper analyses the way of describing architectural space in a form of physical model with correlation of perpendicular projections and it presents selected designing task carried within the subject Descriptive Geometry for the first semester of studies at the Faculty of Architecture. The intent is to incorporate a component of entertainment to break out of the „rigid” and „dry” way of teaching this subject.

Modern education systems and curricula attend are largely based on the application of new technologies. The traditional way of working on subjects from group based on engineering drawing using computers includes adequate theoretical training and practical exercises which are solved by drawing and constructing a pen and aids on paper. The modern method has brought numerous news. The tasks that were solved with a pen on paper, in this case, are solved by using computers and appropriate software tools. There has been a wide acceptance of CAD software packages. Spatial visualization skills is the ability to which it is the application of new technologies and specialized software had both a positive and a negative impact. Due to the great importance of this skill in all areas of engineering, it is necessary to work on its improvement. This present study was designed to determine challenges and promises of mobile devices usage for spatial visualization skills and achievement in Technical Drawing for Engineering course for students at University of Belgrade.

This relates to a basic modelling, the most important assignment for the design beginners with their desires to become designers, to study initially right after entering colleges and universities. The purpose of this research is to clarify the leaders’ tasks in the learning process of 3D spatial perception and 3D construction method for design beginners and deepen the knowledge of the basic modelling education. The research method is to report the assignments set in basic modelling curriculums for design beginners, and to analyze self-evaluation by free description on production of works performed after each assignment completion, based on their grades. In this respect, we have been able to point out the idea of guidance to emphasize the relationship between “Golden Ratio” and “Ratio” to students who are perplexed in shaping in production and to explain them individually. This research result enables to presume clarifying the acquisition effect in the learning process of basic modelling education and the task of the leader side by analyzing the self-evaluation on the work.

The relevance of this study is determined by absence of fundamental research in the use of flipped learning model (FLM) in teaching students of engineering universities Descriptive Geometry, Engineering and Computer Graphics (DGECG); by the absence of scientifically-based, tried and tested programs and teaching materials for DGECG FLM; as well as by the need of development of new, modern tools to support classroom work and forms of students’ individual work. The purpose of this study was to describe the current state of theory and practice in the field of DGECG educational process, which uses flipped concept of learning as a major pedagogical strategy. The main task was the following—to discuss the effectiveness of FLM, its advantages and disadvantages compared to traditional teaching method. The FLM approach has gained increasing popularity not only in schools but also in engineering universities. FLM creates opportunities for solutions of complex pedagogic problems in engineering education but creates some difficulties in preparing for the implementation of the model. Theoretical and practical contribution of the article materials—the synthesis of qualitative and quantitative researches of engineering courses which use a FLM. The study showed that the issues of DGECG FLM have not been investigated in the scientific and methodological literature. To create reasonable theoretical bases of pedagogy in the field of DGECG FLM as well as methods of evaluation it is necessary to conduct further scientific researches examining various aspects of the practical implementation of long-term, tried and tested programs and instructional materials for teaching students.

This article presents the potentialities of architectural modeling in the learning process of Fundamentals of Structural Systems Modeling subject—EAU (Escola de Arquitetura e Urbanismo), incorporating new learning methods, making use of circular reference processes. The low quality of the projects in terms of design, representation and compatibility are still the major problems in architecture. Despite of CAD, BIM and other modeling softwares, mistakes have been detected in many types of projects (architecture, structure, building facilities, etc.). The origin of these occurs in a systematic way, due to the lack of knowledge of the structural and digital possibilities, associated with the non-valuation of the modeling systems and the collaborative actions integrated in this process, which can be already experienced at the beginning of the future architect’s education. The experiences and the tasks performed demonstrate that this combination reinforces the theoretical concepts, enhancing significantly the creative potential in integration with the learning of structural systems.

This paper presents the didactic experiences on digital modeling developed in the last three years on Geometry and Architecture course of the 1st year of the Master in Architecture program of the Faculty of Architecture, University of Porto. For several years, this Geometry and Architecture course, was entirely concerned with projective geometry, and its most common representational systems used in architecture. However, since 2015, we decided to update its syllabus with the introduction of 3D modeling within the use of Rhinoceros software. The approach to the topic of three-dimensional modeling was made through the accomplishment of a teamwork in which the students explore Computer Assisted Design (CAD) processes in the study and resolution of geometry themes with impact on architectural design. With that goal, a three-year plan was defined and structured in the exploration of three topics: Anamorphosis, Tessellations and Surfaces. To demonstrate this didactic strategy and methodology, it is described in greater detail the experience dedicated to the Anamorphosis theme. As conclusion, the full paper acknowledges the success of these didactic experiences on the students engagement with the challenges, the potential of digital tools to support design development and the opportunity opened by the digital modeling on geometry teaching.

As a new educational mode, it is driving changes in teaching content, methods, models and teaching management by MOOC. It brings opportunities and challenges to the reform of education and teaching in Colleges and Universities in China. In this article, It is introduced about the construction of two MOOC courses and the practice of the MOOC-based mixed teaching mode for engineering graphics in Beijing Institute of Technology. It covers the characteristics of the MOOC curriculum and the features of online and offline mixed teaching Mode with these two MOOCs. It takes full advantage of the advantages of both traditional classroom teaching and online teaching by this MOOC-based Mixed teaching mode. It also pays more attention to students’ self-learning and ability development. It focuses on “student-centered” education concept. A mixed teaching system with online and offline is established. A new relationship between teaching and learning is explored. After 3 years of operation, it has achieved student recognition.

This paper has two aims. On the one hand, it aims to offer a brief overview of the history of graph theory applications in the fields of music theory and musicology. On the other hand, it presents an original modelisation by the Authors—developed within the distinctive framework of graph theory in order to represent music objects related to harmony—that could be of particular value to music theorists and composers and that aims to generalize many models so far introduced.

The unpublished treatise by Matteo Zaccolini, Teatin father, painter and teacher of perspective, was composed in Rome in the first quarter of the seventeenth century and is composed by four books. The fourth book, entitled “The delineation of the shadow produced by opaque rectilinear bodies above the flat surface”, is dedicated to the projection of the shadows in perspective representation and is the most interesting for the history of scientific representation as it collects a vast catalogue of examples in which prismatic bodies project shadows on variously oriented flat surfaces, cylinders, cones and spheres. The projection of shadows produced by extended and multiple light sources and the knowledge of conic curves as planar sections of quadratic surfaces is also addressed. The graphic equipment is rich and characterized by the double draft of each drawing: the first version, drafted only by the shape’s outline, shows all the construction lines; the second version, characterized by the chiaroscuro, hasn’t any construction lines. The in-depth critical analisys of the volume allowed to give Zaccolini back a significant role in the panorama of the history of the science of representation in reference to the study of shadows in the perspective projection.

This paper concentrates on the shared experiments on optics, light and acoustics in the 16th century. Most of the scholars involved in this topic have considered the physical behavior of light diffusion to be similar to the sound. According to the direct, catoptric and dioptric observation, propagation of light was used to explain the phenomenon of visual perception and investigate the behavior of visual rays too. These researches were supported by the specific properties connected to the curves obtained by sectioning a cone: ellipse, parabola and hyperbole. Since the importance of religious aspects and the progress of sacred and secular music at the time, the use of geometry allowed the best diffusion of sound through the revolution of two-dimensional conical sections. This happened in order to create three-dimensional architectonical surfaces improved for the best acoustics. One of the most peculiar example can be identified in an unrealized project for a scientific villa arising from the collaboration between Borromini and the monk Emmanuel Maignan. Here some rooms were designed to stress the auditory perception of the visitors. Using digital tools dedicated to light and sound simulation it will be represented and demonstrated the relationship between sound and light.

The Santa Maria Maggiore Choir factory in Bergamo is an exemplary case that clearly illustrates the combination between artistic vitality and craftsmanship that distinguishes the history of Italian art. Typologically this artwork, made at the beginning of the 500 by the painter Lorenzo Lotto and the master inlayer Giovan Francesco Capoferri, is characterized by a series of innovative solutions that make it unique. The choir, built in walnut with the exception of coniferous wood structure, brings together in a single plan seating of the clergy, the benches beside the altar where there are celebrants and public representations of the state and the benches of city delegation, placed in the hemicycle of the apse behind the altar. Within the representation of political and civil power, therefore assumes a pre-eminent position with respect to the clergy, it differs considerably from the ecclesiastical tradition. The work is also famous for the 32 inlays representing Old Testament episodes that characterize the backrest. Some of these have already been investigated in previous works [Buratti, 2013; Buratti 2016; Buratti 2017], while this paper focuses on the inlay L’Annunciazione. This writing is to be considered a fundamental tile of a broader research that has as its final aim in construction of contents useful for the communication of a cultural asset that is difficult to see. The inlays, in fact, given the particular positioning on the backrest, are usually covered by a protective tile that does not allow the vision to visitors.

Stereotomy has always been a subject matter of speculation by scholars who have been involved in Descriptive Geometry. It is well known, in fact, how the latter has its roots in the trait art. Part of proceedings that Gaspard Monge will theorize at the end of 18th century, were commonly used previously to solve dimensional and angular implicit problems of the science of cutting stone. In 1567 in Paris, the French architect Philibert de l’Orme published The Premier Tome of Architecture. The volume made up of nine books, it is an architecture treatise which contains two books, the Livre III and the Livre IIII, devoted to the art of trait. The topic of this essay will be the decryption and the translation—in a contemporary key, according to the tools provided by the modern Descriptive Geometry and by the current digital modelers—of one of the trait contained within the two books mentioned above. The aim of this essay is to verify the one-to-one relationship that exists between the object and his representation, therefore the correspondence that there is between de l’Orme’s graphics language and Monge’s projective processes of one trait concerning vault proposed in the treatise. The verification of this connection will be done by means of the use of digital space models of the architectonical objects examined by the French author. The surfaces connected to them will be digitally proposed again and, with them you will showed the operations of rabatment, translation and/or proto-projective that could render evident de l’Orme’s representative universe.

The practical treatise of perspective (1613) is undoubtedly one of the less studied treatise, although there are some innovative aspects that are much earlier than the actual coding of perspective science. Filippo Camerota published and commented the Cigoli’s treatise in his “Linear Perspective in the age of Galileo. Ludovico Cigoli’s Prospettiva Pratica” and filled an empty space concerning Cigoli’s contribution to the development of perspective. Camerota has highlighted many innovative aspects of the treaty, the profound knowledge of the perspective science of the treatise expressed in the first two rules, and confirmed by the third rule that, through the analysis, study and construction of a perspective machine, has allowed to confirm and endorse the first two. However, there remains a gap concerning the singular use of canonical distance points by the Cigoli, which makes it an innovative use especially in the second book, with reference to the second perspective rule, for the visualization of the fake facades of a theatrical backdrop in true form, in order to recreate, from the noble point of view, a three-dimensional illusion. Exactly this is the theme analyzed in this paper, through the use of computer graphics to better render the study and the underlying results.

What do some children’s books today have in common with English perspectives treatises of the seventeenth and eighteenth centuries? The answer lies in the fact that they both use alternative strategies for three-dimensional spatial rendering. These treatises, in fact, contain some mobile inserts that transform two-dimensional drawings into true 3D models, allowing the reader to immediately understand the spatial nature of a phenomenon such as the generation of perspective projections. English perspective literature arrived somewhat later in embracing the advances achieved in previous centuries in Italy and France on perspective. However, it does reveal a distinct approach in the development of graphic apparatus, essential for understanding the contents of this field of study. These approaches are useful in explaining the fundamentals of perspective but also in seeing the effects of the mutual movement of reference elements, subjects and observer. The most direct ancestor of these perspective texts can be found in books that belong to different fields as Geometry and Cryptography, using moveable elements to clarify or add new significances to the treatises they host.

In 1729 the Dutch cartographer Nicolaas Cruquius engraved a map that became a benchmark for every future illustration of a territory. The map, showing the bed of the river Merwede and its surroundings, was made to control an area subject to inundation and flooding, understand the territory, and plan projects to solve the thorny problem of water management. In this superb map, divided into two tables, Cruquius adopts contour lines of equal value. This was a first. What Cruquius did was reinterpret and reuse the isogones employed roughly thirty years earlier by another scientist to represent a physical phenomenon, and then use them in a different context. In fact, in 1701 Edmund Halley had employed isogones in a map he drew to describe magnetic declination over the ocean. Halley and Cruquius use lines of equal value to describe two very different models (one is a physical phenomenon; the other is an orographic model). However, they both helped to legitimise the use of contour lines to represent geographically-based phenomena. In 1712 Cruquius had made an accurate map of Delfland. This extremely precise map reveals contamination between zenithal projection and perspective view, both of which sometimes appear in the same table in a seamless shift from one projective mode to another. The simultaneous presence of different projective methods was inspired by sixteenth- and seventeenth-century maps. The method creates images that are accurate, measurable, and captivating at the same time, but they are a far cry from the projective integrity that cartography was to acquire during the eighteenth century. Cruquius adopts isobaths to maintain the plastic effect in a zenithal projection, but abandons them in the secondary tributaries where he uses more conventional graphics which were inspired by earlier examples and were to become quite common to portray water flowing along rivers. A similar graphic depiction of water is present in the zenithal plan of Rome by Giovanni Battista Nolli engraved just nineteen years after the Merwede map. The way in which natural elements are represented in Nolli’s map, the accurate measurements, and deliberate rejection of central or pseudo-axonometric projection, warrant a comparison between Curquius’ impressive map and the one made by Nolli.

The success of the Quincunx plan in the religious architecture of 15th and 16th century Italy is generally related to the suggestions coming from some monumental sacred buildings, from the places where these buildings are located and their ancient and oriental origin. Added to this, this scheme demonstrated an ability to adapt to different sites and themes and to be contaminated by forms and types coming from distant sources. Some of Leonardo da Vinci’s studies on centralized temples, which are collected in the Codex B at the Institute de France, in the Codex Ashburnham 2037, and in the Codex Atlanticus, testify above all the value of the Quincunx as a flexible geometric and compositional device with great semantic and didactic potential, providing a medium for the subsequent 16th century developments by Bramante and his Roman followers.

This study investigates architectural survey practices between the 18th and 19th centuries. Much has been written about the magnificent drawings of the pensionnaires of the French Academy in Rome but very little is known regarding architects’ practical training and about how their surveys were actually carried out. An important source used to trace back to the knowledge and procedures of architects at the time under analysis consists of educational manuals on land surveying that appeared in France at the end of the 18th century. Referring to basic mathematical-geometric proficiency, they provide a framework of the methods and logical procedures of land and architectural surveys. At the beginning of the 19th century there is a widespread proliferation of this type of publication, as testified by the number of manuals found in the Bibliothèque Nationale in Paris. This study is based on a direct examination of more than thirty original volumes, published between 1673 and 1845, that truly testify to the extent of French publishing at the time. In analysing the manuals, the following matters were considered: the addressees and the authors of the manuals, the articulation of their content, the role of geometry, the description of employed instruments, and the explanation of applied methods.

In this work, we approach an example of the construction of bells where formulas for the application of Geometry, often converted into a true “state secret” by their manufacturers, intervene. The bells, religious or civil instruments, also become beautiful musical instruments, which call according to their sonority, different passages of religious life or the announcement of certain circumstances of civil life, dispelling joy, welcome, warning, and most of the time a warm sound of musical concerts that invite you to enjoy what is called “calm”. In the development of the work, we will present the following articles: manufacture of bronze bells, master smelters, main factories of the world; history, epigraphy, iconography, touches and signs of its sonorous meaning; main bell towers in the world, the Cathedral of La Plata, Province of Buenos Aires, Argentina.

Every people, in every historical period, developed methods to measure Time both at a daily scale and at a yearly scale. Some of them constructed sundials to represent the apparent trajectory of the Sun around the Earth, by using and developing tools from descriptive and projective Geometry, mainly. This subject acquired a great multidisciplinary interest since ancient times, also for Science of Representation applications. This study presents the first results of an ongoing research concerning some aspects related to Time Measurement. The geometric-spatial setting of the Sun-Earth system is described and is structured parametrically via algorithms, following the known conventions shared and endorsed by gnomonic treatises. A three-dimensional model built with a strictly geometrical approach was developed; this allowed to set parameters (e.g., the latitude of the site, the Sun declination angle, the hour angle, the altitude and collocation of the Sun relative to the sky) and relations dynamically, which define the variation of the length of day and night during the year. The 3D model allowed an in-depth study of the properties and peculiar characteristics of some sundials and a new variant of a known one is also proposed. The unreleased geometrical constructions in Monge’s orthogonal projections were elaborated using by GeoGebra and the 3D models and algorithmic definitions were developed using by Grasshopper and Ladybug plug-ins, eventually visualising the results in Rhinoceros.

A cultural heritage system about Japanese historical religious ritual called Bugaku Mandala-ku has been developed. It includes digital contents of historical religious site and buildings as well as performances played on it with 3DCG animation. Bugaku Mandala-ku is a religious ritual to pray for national prosperity and a good harvest. This is one of the rare and special cases of syncretism of the Japanese native nature worship Shinto with imported religion Buddhism, and it has not been held for more than 170 years since the late Edo period. The scene of Bugaku Mandala-ku was described in detail in the drawing called Sogon-zu, in which the shape of the stage, position and motion of the performers, and rough scenarios of the Shinto ritual were shown. By referencing these drawings and information provided by the shrine, the precinct of the shrine in the Edo period has been reconstructed with 3DCG. The details of the Bugaku stage has been obtained by referencing the stage which has currently been used, to reconstruct the stage. Since Bugaku performance has been still inherited by some small national and private cultural organizations, the performer’s body motion was able to be captured with a motion capture system, in order to make the 3DCG character animation. Combining these information, recreation of the CG character’s performance on the Bugaku stage situated in the shrine precinct was made possible. Introduction of VR technology into the system and its use as an educational interactive media has also been planned, for helping young people to understand this precious and special Japanese historical intangible properties.

In the 9th century, a new religion that combined Buddhism with mountain worship appeared in Japan, and many mountain temples inspired by this religion were built in Nara Prefecture. The unique site planning of these temples seems to have been devised to encourage faith in visitors. This study aims to identify the characteristics of site planning by analyzing the scenes along the visiting route of each temple, as they change from moment to moment. MOTATION, which was proposed by Lawrence Halprin, is a method for graphically representing the changing appearance of a landscape as a person moves through it. In this research, MOTATION was applied to three mountain temples: Muroji, Hasedera, and Kinpusenji. The visiting route of each temple was described by MOTATION based on videos and pictures. In addition, we graphed and analyzed the relationship between distance, height, and surrounding facilities along the visiting routes. We found that the relationship creates a characteristic scene transition by site-specific planning at each temple. This suggests that such scene transitions were intended to give a spatial impression to visitors.

This paper aims to identify the application of the theory of “Deconstruction” to the architectural field. For that purpose, we make a comparative study through an investigation of the definition by the philosopher Jacques Derrida and the architect Bernard Tschumi. First, this study investigates the descriptions written by two curators, P. Johnson and M. Wigley, in the catalog of an exhibition held at the Museum of Modern Art (MoMA) in New York in order to clarify the definition of “De-constructivism”. Next, this research reveals what Jacques Derrida meant by “deconstruction” by investigating the descriptions written in the book “De la grammatologie” published in 1967. Furthermore, this research clarifies Bernard Tschumi’s architectural theory by investigating the descriptions written in his book “Architecture and Disjunction”, which was published in 1994. In addition, we clarify the influence of Derrida’s deconstruction theory on Tschumi’s building theory through a comparative study. Finally, we clarify the architectural theory that appears in his work by investigating the drawings that were designed by Tschumi in the “Parc de la Villette” project.

This work tries to explore some hidden feature in Chinese Classic Gardens by the perceptual space graphic analysis. Since 17th century, due to Sir. William Temple’s first time and initial introduction, Chinese Classic Gardens had been generally known possessed a remarkable space feature, namely sharawadgi, at western architecture and art field in its time. But by the previous researches, it is a linguistic misunderstanding that sharawadgi was original from a certain speciality Chinese phrase. However, it reflected the surface truth that the artful irregularity and asymmetry in Chinese garden. Moreover, it implied the essential difference between western and Chinese spatial design attitude and principle. This work begins with seeking the reason of the sharawadgi misreading issue, to reveal the special design logic in Chinese Classic Garden. The basic physical data in this paper is collected from Liu Dunzhen’s famous orthogonal drawings, which was done in 1970s, strongly influenced by western classic graphic representation of architecture. While, nowadays, it was criticized that this kind of graphic representation distorted Chinese Classic Gardens’ feature. Therefore, in this work, borrowing the perspective of perception-phenomenology and ideas of visual psychology, by adding the perceptual spatial elements, it tried tries to translate the typical feature, general known as Sharawadgi, to visible graphical diagrams. This will improve its understandability and clean the babel of mutual incomprehension. Moreover, it might provide some innovation ideas for the graphic representation of contemporary architecture, and also for nowadays spatial design.

For each pictorial work it is possible to identify—perhaps even in retrospect—a geometric rigor on which the graphic composition itself is based. Sometimes these geometries are more evident and highlighted by graphic devices that openly declare their existence; other times, on the contrary, they are to be sought through a succession of attempts and experiments aimed at highlighting all that is not seen. The geometric rigor found in Leonardo’s Last Dinner, not only marks the sequence of the characters and their placement, but is also the founding element of the perspective space represented starting from the identification of the simple relationship 2:1. Through attempts and experimentation we can justify with geometry those relations between the parts that make each composition balanced. With the same attention and with the same means we can investigate any graphic composition belonging to the world of painting or any other visual art. This also applies to advertising graphics products that take on an even more interesting role when considered in the historical context between the nineteenth and twentieth centuries, when we witness the birth of modern advertising thanks to the diffusion of Affiches.

In frame of the technical session “Geometry and Graphics in History” in the subsection “Masters and Pioneers”, we reviewed the activities of the famous Italian Leonardo da Vinci and analyzed how his activities were evaluated in Russia at different times. What was the attitude of the Russian people to the Italian genius? How changed has the attitude to him and his activities in different historical periods? Over the last 3 centuries in Russia the revolution took place, changed the state system, came to power various rulers, and the life of the Russian people overturned three times. The authors of the article made an analysis of the encyclopedic literature, which was preserved in special storages facilities since czarist times. The results of the analysis were startling! Under such global state changes, when many Russian scientists became persecuted and subjected to harsh criticism, the Russian people opinion about the Italian Legend has always remained the same. In Imperial Russia and the Soviet Union, and now Russian people have always loved and revered by Leonardo for his work, for the diversity of his personality, his talent and ability. Never, nobody and not once, did doubt the genius of this Great scientist. This was due to the fact that Leonardo was not just a genius Italian painter. He was a multifaceted outstanding scientist of the World! His projects and sketches nudge to scientists around the world pushed to make new discoveries and inventions for the benefit of humanity.

In the XVII century the scientific debate revolved around the celestial wonders considered as mere application of terrestrial geometries. At the time Rome, one of the most important European theater of experimental science, had a large group of international scholars and, among them, Athanasius Kircher collaborated intensively on the transformation of the Jesuit College into an important center of scientific activity. He promoted the poetics of wonder, typical of the baroque art, as well as the philosophical and scientific temper which laid the foundations of the experimental method. This essay will deal with light and shadow projections in Kircher’s sundials, focusing on the problem of intersection between surfaces. Kircher’s sundials, basing on Optics, oversee and translate reality in mathematical terms becoming a scientific tool for the knowledge of the celestial mathematical rules and they are also an essential means for recreating empirically, experimentally, mechanically the perpetual motion of the universe. If on one hand their construction are based on the same rules of perspectiva artificialis, used by painters, on the other the symbolic function of sundials silently celebrates the encounter between light and shadow, sky and earth, space and time, configuring the epiphany of physical realities.

This study focused on the method of designing original motifs and patterns through analog and digital means. The design of Japanese craft products, including their shapes, colors, decorative motifs and patterns is here referred to as “Zuan”. This study established the method of using sensibility and imaginations in the process of depicting drawing rather than sketching the object directly. It also focused on the application of rough geometric illustrations that are used to simplify and harmonize the shape of objects in the creation of a crest as seen in “zuan” education. At the preliminary stage of the design process, 10 s drawing method was suggested and “zuan” geometric baseline was used to derive sketches of simple motifs and shapes. Three types of design method using geometric baselines were considered in this study. The effects to expand the imagination of design shapes and their tendency was shown. The baselines were finally analyzed to determine their visual effects.

Starting from the impact, which the École Polytechnique had on higher educations in Europe, this paper wants to highlight the role of material models especially for teaching mathematics. Models of ruled surfaces play a prominent role in this narrative, since Gaspard Monge, who taught “Géometrie descriptive” in Paris between 1794 and 1816, already used string models to support his lectures. For this reason, we want to trace especially the history of ruled surface models from the late 18th century to the presence. The investigation focuses on persons, used materials and the major topics. It is known that the axiomatization of mathematics lead to a decay of the meaning of material models in the early 20th century. But at the same time, material mathematical models gained relevance in other disciplines like civil engineering and art. We also want to show, how ruled surfaces can be part of current teaching projects.

We aim at introducing comments and details on the role of Mathematics in the development of well-known challenging structures. In particular, we focus on masonry domes (and arches), since they can be considered landmarks in the history of Architecture.

The research carried out in the Surveying of Architecture and the City course in the School of Architecture and Design at the University of Camerino studies the presence of small theatres in Italian towns. The historical period examined is the seventeenth and eighteenth centuries, an age that saw the growth of the culture of theatre performance. The territory where the theatres are located is the Marche Region, which contains interesting architectural examples. For each building, a survey campaign was made using direct and indirect methods. The material gathered was then processed in the studio. The orthographic views of the cardinal directions and the sections allowed the state of conservation to be analysed. The rendering of decorative details in a synoptic panel allowed the stylistic choices adopted by each designer to be observed. Three-dimensional models of the theatres were made in order to show the relationships among the parts and between the building and the urban context. To understand the role of these buildings, an illustrative city centre was also surveyed. All urban sectors in this small town were studied using direct and indirect surveys with laser scans and photogrammetry, and the data acquired were reproduced in orthographic and axonometric projections. The research investigates problems related to the use of various surveying methods applied to real case studies. It also reflects on the theatre and its construction in small urban centres, as it represents an important moment for the city and its residents, involving different local workers (painters, masons, architects, etc.).

Geometry has historically dealt very often, notably in sculpture, with proportional relationships of the human body but it has not always faced, with the same intensity, a similar balanced representation of the horse. In any case different approaches can be reported. If Leonardo used a field survey to build a horse model, a research with more scientific ambitions dates back to Morris’s theory of joint angles. The analysis of the monument designed by Michelangelo for Henry II of France reveals nevertheless a complex origin in the neo-platonic poetics as well as a dialectic between mind, matter, spirit and body. Michelangelesque aesthetics is deeply rooted in the rediscovery of Plotinus’ doctrine about the search for unity and in the awakening of the “inner light”. The analysis of what remains of the project goes through an approximation of the artist’s sign with three-dimensional figures so far as to shape a verisimilar digital model, which is also based on other works of the same author, to reconstruct what could have been a great realization of the Renaissance.

Between the Renaissance and Baroque, perspective is a privileged form of representation of reality. While mathematical speculation contributed to making perspective an exact science, it was widely practiced in different forms of artistic expression. The problems linked to the operational practice concerned all its applications in a transversal way, from scenography and anamorphoses to the illusory perspective. Methods of constructing perspective traces are generally described in the treatises on practical perspective in a fragmentary way. Abraham Bosse is the author of a volume published in 1653, entitled Moyen universel de pratiquer la perspective sur les tableaux ou surfaces irrégulières, entirely dedicated to the method for reproducing perspective traces on architectural surfaces. In Bosse’s work, the problem of perspective construction is addressed according to the levels of increasing complexity in which the picture plane, starting from its flat or generically inclined configuration, assumes a completely irregular morphology. The proposed procedure is universal and resolves the question through the method of perspective Arguesian scales, without using inaccessible “vanishing points”. Bosse imagines the construction of perspective on the vertical walls, considered infinitely extended, of the room to be painted, overlapping it with a regular grid. Then, he imagines projecting this grid from the same projection center onto any picture plane. The operational practice makes use of the construction of a picture plane that we can define ‘auxiliary’, reproduced by the ropes used in the construction and projected on the surfaces to be painted.

As any language, the language of architecture is characterized by specific qualities based on certain norms and regulations. During many centuries, the order has been considered as a central category connecting all the conceptions of the architectural language. In the second half of 1st century BC, a Roman architect Vitruvius asserted fundamentals of the modern architectural values in his treatise “The Ten Books on Architecture”, based on the rules of harmony. The key point of the treatise is the Vitruvian Triad—«firmitas, utilitas, venustas» (strength, utility, beauty). However, the modern rhythms of our society dictate new requirements for the architecture. The development of society is characterized, first, sufficient information richness in knowledge, production methods and technologies, materials, second, the globality of communication possibilities: plurality and accessibility of information sources transfer of innovation, high technology manufacturing, intelligent products. Such changes should affect the appearance of new concepts and styles in architecture, the changing goals and objectives, as well as ways and methods of their realization. Continuous flow of innovations change consumer needs, determine new fundamental aspects of architectural work. Therefore, “innovation” is a new fourth category modern fundamentals of architectural values. The article presents the innovative aspects of architectural activity, confirming the hypothesis of the emergence of a new category.

The Modo di misurare le fabriche (1674), by Guarino Guarini is a treatise devoted to the explanation of methods to calculate surfaces and volumes. This treatise is one of the least studied among Guarini’s theoretical works. Referring to Euclides adauctus (1671), Guarini expresses the desire to make the geometric principles developed therein applicable and accessible, providing methods of measurement of works under construction in the second expansion of the Baroque city. The second part of the book, which is dedicated to the calculation of 3D surfaces, constantly refers to the intradosal surfaces of the vaults that constitute the prevailing cover of the coeval atria, main halls, and rooms. In the treatise, the elements that make up the vaulted systems (coves, groins, and domes) are reduced to the elementary geometries that shape them. The different sections, together with the combination of different shapes, offer examples on which Guarini proposes new exact or approximate calculation methods. Previously, the author carried out a reconstructive modeling on the XIX and XX plates of the Architettura civile, which allowed identifying a real vocabulary of shapes that can be used to generate multiple composed vaulted systems. Three-dimensional digital modeling, realized for the present research on Guarini graphic schemes, allows us: to verify the degree of accuracy of the proposed calculation methods, by comparing the analytical calculation of the surfaces applying Guarini’s formulas and the automatic calculation offered by the modeling software; and to compare and enrich (with new shapes) the casuistry present in the Architettura civile.

The discovery of prehistoric pile dwellings in nineteenth-century Switzerland was enthusiastically welcomed by Swiss citizens. Based on the results of an excavation survey, in the 1920s, pile dwellings were reconstructed at Unteruhldingen, a small lakeside town by Lake Constance. This study clarifies the influence of the discovery of prehistoric pile dwellings on the architectural works of the modern Swiss architect Hannes Meyer (1889–1954), the second director of the Bauhaus. In terms of methodology, Sect. 2 outlines the process of reconstruction of pile dwellings around the Alps until the 1920s, and in Sect. 3, we analyze the influence of the pile dwellings on Meyer’s three major works in the 1920s based on both the architectural form and the design concept. As research materials, we used drawings and design concepts obtained from publication materials. From the drawing of the “Peters Schule” competition project (1926–27) and the ground floor plan of the “League of Nations” project, we can recognize that the buildings float upon pillars resembling piles of pile dwellings. In his masterpiece “ADGB Trade Union School” (1928–1930), Meyer finally explained the design concept using the word “modern pile-dwellers.” Thus, we can prove that the discovery of the pile-dwellings around the Alps and the subsequent reconstructions of the dwellings had influenced Meyer’s architectural design in the latter half of the 1920s.

Physical models have always been the most exhaustive and suggestive documents to transmit and understand the morphological characteristics of an architectural subject and reveal their state of knowledge in a given period. The two main models that Carlo Lucangeli, architect and cabinetmaker who lived between the 18th and 19th centuries, dedicates to the Flavian Amphitheater are among the most important in the history of the monument representation, since one—made of cork—records its appearance in a specific epoch, the other—made of wood—is an interesting reconstructive hypothesis of the ideal state. In particular, this second model, realized in the space of 22 years, is striking for the scientificity with which it communicates the characteristics of the subject, distinguishing itself from the modeling tradition of that time: in fact, he decompose the model not only to facilitate its assembly and disassembly, but also to communicate the structural, functional and aesthetic characteristics of the monument by proposing a clear and original reading. This study first analyzes the communicative capacity of the model, as a three-dimensional technical drawing, and produces original observations on what the model reproduces by direct knowledge, and what is instead the result of interpretation, in relation to the critical tradition on the subject, retrace the famous testimonies of Carlo Fontana and Antoine Desgodets.

This research project focuses on the VR simulation of the Giant Wild Goose Pagoda (Dayanta) in southern Xi’an, Shaanxi province, China, as an investigative subject for the use of virtual reality and digital simulation in engineering graphics. The Giant Wild Goose Pagoda is a typical Chinese pagoda built in AD 652, during the Tang Dynasty (from AD 618 to 907); because the Tang Dynasty is regarded as the most prosperous and magnificent dynasty in Chinese history, the buildings constructed during this period have frequently been referenced in Chinese architecture since then. The VR simulation presented in this research is intended to show the uniqueness of the complexity of the structure of the Giant Wild Goose Pagoda as well as the beauty of structural and landscape design principles dating back to the Tang Dynasty. Firstly, using modern graphical technology, the authors completed a 3D model of the Dayanta, through which to create a 3D database by translation from 2D drawings and literature documentation. Secondly, the authors used Lumion as the advanced rendering tool to build the dynamic environment. To create the environment around the pagoda, the authors added natural scenery elements such as vegetation and terrain features from the natural libraries, and to make the elements more realistic for the scale of the model, the authors then made adjustments for the size of the elements. Lastly, the authors employed the Unity VR package to create an immersive experience inside the pagoda for viewing the structure.

The golden ratio has universal application and provides maximum performance in an artistic composition. This article discusses how knowledge about golden ratio can be used in jewelry design. The golden rectangle and golden pentagon were used as grids to generate jewelry with harmonic proportions.

The paper deals with the results of a research activity related to the application of BIM technologies for the analysis of seismic risk in existing school buildings. Digital modelling was carried up in phases, organizing the various disciplinary models according to a federated model approach. The case study highlighted potential and criticality in the generation of integrated architectural, structural and analytical models, and in the development of the information data flow, on which the reliability of the simulations of structural behavior depends.

The Wallace-Simson line is the line containing the feet of the lines perpendicular from an arbitrary point on the circumcircle of a triangle to the sides of the triangle. The line was attributed to R. Simson by J. V. Poncelet, but today it is usually known as the Wallace-Simson line since the term was introduced by W. Wallace in 1797 and it does not actually appear in any work of Simson. Various interesting properties are known such as that the set of all of the Wallace-Simson lines for a given triangle form an envelope of a deltoid which is known as the Steiners deltoid. In this work we will treat the Wallace-Simson line and Steiners deltoid, except in the Euclidean plane, as well as in three other Cayley-Klein planes: the quasi-elliptic, the pseudo-Euclidean and the quasi-hyperbolic plane.

The present work discusses solutions of the axonometric, positional and metric problems within a design-technological cycle of manufacturing parts with curvilinear channels. On the basis of the early developed general approach, the geometrical engineering problems of various types are solved. The work includes algorithm and the graphical solution of the positional problem raised in the construction of the intersection lines of a curvilinear cylindrical surface with a conic surface. The proposed complex solution of positional and axonometric problems results in the construction of a three-dimensional model of conjugation of the curvilinear surfaces of channels in the part.

The following submission is about the creative process behind the 3D modelling of the logo for the ICGG 2018 Conference, based on the concept designed by Professor Luigi Cocchiarella (Politecnico di Milano, Italy). The work focused on the possibilities given by parametric modelling into the logo design workflow. After the creation of an algorithm able to create the basics shapes of the logo from a set of input values, different combinations of parameters were tested in search of a pleasant result, during which both the logo and the algorithm were polished in a mutual beneficial relationship.

The Alexander Mosaic and the House of the Faun in Pompeii hide the traces of a compositional, a painstaking process of calculation and precision based on regulators, even surprising symmetries, and aesthetic precision.

This report is presenting partial results of the wider field research on spatial abilities conducted at a specifically chosen group of freshmen level students at the Faculty of Architecture, Cracow University of Technology. Only two aspects of the research have been reported: gender differences and evaluation procedure analysis in context to the earlier results. MRT has been used as a research tool, ANOVA variance analysis for the repeated measurements (mixed models) has been applied in order to evaluate gender differences with the assumed value p < 0.05. Conclusions has been drawn as men characterize better skills in mental rotations if compared to women. It has been also confirmed that the results on MRT depend on the method of the test grading.

Research on methods for representing natural objects and phenomena by computer graphics (CG) has been steadily broadening the scope of represented objects. In expressing the natural landscape by CG, the topography is one of the important research subjects as a basic landscape component. Authoring virtual terrains presents a challenge and there is a strong need for authoring tools able to create realistic terrains. In this research, we propose a method to define an initial terrain model and perform erosion simulation. A general topographic shape generation method is a surface with undulations from information of height stored in two-dimensional array data called height field. However, with this data structure it is difficult to express the weathering structure called Toppling failure and the terrain such as the cliffs and caverns made by erosion due to the intense erosion of the waves. On the other hand, although volume data can define the internal structure of an object, defining and processing all of the large terrain with volume data has a problem of increasing the size of the data. In this method, we simulate the erosion process of terrain by combining terrain data generated from height field and volume data storing concentration value.

Three-dimensional CAD (Computer Aided Design) software can be used to analyze phenomena related to movement such as vibration and friction. But this requires knowledge for handling material properties and uses special three-dimensional CAD functionality. For these reasons, analysis based on three-dimensional CAD of phenomena is greatly influenced by skill level in model design and enormous time if required due to processing of analysis. Therefore, it is difficult to treat as an auxiliary tool for analysis. Also, various software exist as three-dimensional CAD, but each software varies in method of use. In addition, automatically obtained finite element mesh data in analysis differs depending on software. Therefore, even with the same model, it is difficult to analyze under the same conditions and to obtain the same result [14]. In this paper, we will study the method for analyzing the lubrication phenomena. From this study we will propose a method easy even for beginners, and show that the analysis method is simple and quick and reduces the burden on the designer.

In 2012 Pottmann et al. presented full classification of 3-webs (hexagonal webs) of circles on Darboux cyclides into 5 types. We provide rational trigonometric bilinear parametrizations of these webs of circles in all cases except for the general case of type 3, which has a parametrization involving square root. As a direct corollary, analytic formulas for discrete 3-webs can be easily extracted from these parametrizations.

The report analyses how to better proceed from general discussion on graphic literacy in engineering education, by differentiating between the different types of engineering drawings, from the semiotic point of view, which has inductive reasoning and plays an explanatory role. In the long history of visualization in engineering graphics one has gained (presented) new ideas for solving problems (Plans and architectural drawings in Ancient Egypt, http://www.ucl.ac.uk/museeums-static/digitalegypt/architecture/plans.html, [1]) and drawing is one of the oldest engineering disciplines. Real products are manufactured on the basic of engineering drawings. Engineering and technology students learn basic knowledge, in order compose engineering drawings as reflections of existing objects or concepts of future objects, within the Engineering Graphics course. The development of Engineering Graphics is influenced (besides other theories) by semiotics—the study of signs and symbols. Peirce’s triadic model can help encode and decode signs for which there international agreement that excludes different interpretations and includes the study of how meaning is constructed and understood (http://www.newworldencyclopedia.org/entery/Semiotics, [2]).

In 1496 Fra Pacioli’s fame led to an invitation to join the court of Ludovico Sforza in Milan. Here Luca met Leonardo da Vinci and taught Leonardo the intricacies of geometry and in the meantime Leonardo informed Pacioli of the application of geometry to art and Architecture. The text of De Divina Proportione clearly depended on the close collaboration of these two Renaissance scholars. Leonardo himself drew the geometrical illustrations for the manuscript. In 1509 Pacioli published De Divina Proportione, integrated with the Tractato del’architectura, that begins with a discussion on the proportions of the human body. In this edition, Luca fits the tables with the construction of the capital letters. Pacioli’s alphabet is based on the same square and circle construction that had guided Leon Battista Alberti. We felt that this beautiful alphabet needed to be restored and we set out to construct an accurate replica with GeoGebra, using the Pacioli’s instructions although it was incomplete.

The purpose of this article is research of geometry and 3D modelling on decorated ceilings of Vilnius Cathedral. The issues which this paper focuses on are the analyses carried out by geometrical data management, intended to prepare digital library of classical ceiling parts. There were few stages of research described in paper. First of all—historical issues of object, after is the analysis of geometrical and graphical features of ceiling artistry, and then study of development of a web-based application for users and interactive exploration of three dimensional models. The ideas about history, visuality and perception, emotion, modelling and virtuality are described at this study. Overall approach was to create an application for tourists, historians and students, where they can find not only information about main tourism objects, but also digital models of a ceilings rosettes, particularly situated in places out of reach for visitors too.

“Rakuchu Rakugai-zu” are paintings of scenes in and around the capital of Kyoto with a detailed interest in figures and buildings on folding screens. Famous sites, festivals and activities within rakuchu and its surroundings rakugai are presented in a composition typically depicting the scene by a bird’s-eye view. Many of them are produced from Muromachi period to Edo period. The expression reflects the depicted period. In this study, I analyzed two works of Rakuchu Rakugai-zu painted in different times and compared them on characteristic expression. As a result, representations of buildings on the picture plane are drawn mostly by oblique projection. The expression in the first stage depicts wide space, the panorama of the whole of Kyoto when the viewers are surrounded by a pair of folding screens. On the other hand, the expression in the second stage depicts limited space, which looks like a theater stage when the person confronts a pair of folding screens face on words.

The aim is not to create gracious drawings but clarifying models of concrete problems without excluding theoretical research and pure creativity. The experience as a lecturer of representation has enabled me to notice the obstacles that students meet when imagining the geometrical entities (lines/curves, figures/volumes) if thought of in oriented space and their relative problems of representation/measurements. The basis of the study that I present as a contribution, is the preventive evaluation of the difficulty of geometrical problems or geometrical entities that enable the determination of the geometrical model to represent and, consequently, the combination and succession of chapters. Important problems and relative applications are interspersed considering the method adequate for representation and relative intrinsic complexity. Wherever there is in place a pragmatic teaching, based on the levels of knowledge, the students that intend to follow a university design course are expected to have advanced levels in scientific subjects but nothing relative to the field of visual arts. The difficulty for the lecturers of representation lies in the fact that, in a short period of time, the gap in general knowledge must be filled and the theoretical/practical knowledge useful for the construction of the models relative to the design exercises must be given.

The use of software for digital modeling is increasingly widespread in colleges and architecture offices and allows to develop a project from its conceptual stage to the executive details. In the present article, the most used software in the initial phase of the project is studied, that is, those suitable for the creative development of the architectonical form, in this sense were chosen Sketchup, Rhinoceros and 3D Studio Max. To materialize the exploration carried out through experimentation and to level the process on different platforms, the Brasilia Cathedral was chosen as the base model. As an example of the style of one of the most renowned architects of Brazilian modernism, Oscar Niemeyer, this construction encompasses formal, spatial qualities valued by three-dimensional perception. The reproduction of digital models of the Cathedral of Brasilia, a work already constructed, will be useful for teaching and learning, providing a comparison with the real object, which inspires the improvement of the virtual model.

The work here presented concerns the realization of a MOOC hosted by a platform (www.europeanmoocs.eu), developed by the University of Naples Federico II under a CIP European Program, offering services to a variety of instructional designs and pedagogical approaches. The online course concerns an important chapter of projective geometry, commonly known as “The Theory of Shadows”, which participants have to learn in order to draw the lights and shadows of space objects—from simple plane figures, to more complex geometrical solids and elements of architecture—correctly. The focus is on the essence of the discipline of drawing—exercising creativity and giving free space for students to express themselves. In order to maximize students’ learning in creative way, we have created a MOOC, comprising two main components: contents and pedagogical design, as a software package. More particularly, learning design puts the learning journey at the heart of the design process and provides a set of tools and information to support a learner activity-based approach. In our experience, we can’t say that a MOOC is the best way of teaching graphic education, but we can say that is the most improved one.

Pedro II School, which is located in Rio de Janeiro, Brazil, and was founded in 1837, is a traditional institution in education and is also recognized for its excellence. Said School is responsible for the formation of citizens who are capable of acting in the job market. Since the foundation of the School, the Drawing subject is mandatory, therefore this article brings to the discussion the importance of the teaching of Drawing in Basic Education by acquiring graphic skills and how such skills are processed in logical and spatial deductive thinking. The aforesaid knowledge, which was acquired by the former student Mr. Caio Pereira, corroborated in his professional environment considering its apprehension and allowed its application in the following exhibition: “Rolé pelo Rio Hackeado” (in English “A walk around Hacked Rio”) with the Motion graffiti entitled “Preto Velho” (in English “Old Black Man”) in the Museum of Tomorrow in Rio de Janeiro, Brazil. The author, besides the geometrographic knowledge in the development of the work, has appropriated himself of technological software languages using parametric concepts by having the shapes of the polygons, polyhedra and conic curves in his projection, thus reaching its goal of causing restlessness in the visitor of the museum by the magic of the scene.

Constructability of new ruled surfaces is expanded with employing the “Kinematical Surfaces” model [1]. In the context of development of the recently proposed geometrical model for constructing kinematical ruled surfaces based on interrelated movements in matched triads of contacted axoids [2], the analytical representation of constructing kinematical ruled surfaces for a new composition of the axoids’ triad “torse—circular cone—circular cone” is worked out in this research. The substance of the proposed geometrical model of interrelated movements in matched triads of contacted axoids, where one of them is a fixed axoid and two other are moving axoids, consists in the correspondence between the movement of the first moving axoid along the fixed axoid and the movement of the second moving axoid along the first moving axoid [2]. Some examples of the application of the proposed model have been realized on the base of triads: “cylinder–cylinder–cylinder”, “cone–cone–cone”, etc. [2]. The geometrical model for the new composition of the axoids’ triad “torse–circular cone–circular cone”, in which the torse surface with the cuspidal edge in the form of the circular cylindrical helical line is used as a fixed axoid, and two circular cone surfaces as moving axoids, is developed in this research. The analytical representation and computer visualization of constructed kinematical ruled surfaces is realized for the proposed axoids’ triad.

Emaki is a traditional Japanese pictorial expression format. Emaki (“picture scrolls”) are viewed using the unique characteristics of scrolls. The viewer does not look at the paintings from the start to the end, but rather reveals them gradually by unravelling the scroll. Emaki content can be broadly categorized into two types: narrative emaki and religious emaki. Kasuga Gongen Genki and Ishiyama-dera Engi, the subjects of this analysis, are religious emaki from the Kamakura Period, during which the emaki culture developed and a diverse range of works were produced. These emaki are attributed to Takashina Takakane, a renowned and greatly talented imperial court artist. These emaki include many scenes depicting backgrounds with shrines, temples, residences, and other buildings in oblique projections. Accordingly, the front, sides, and top are drawn for sections with buildings, and the characters in the narrative are placed on one of these three locations. As a result, one gets a glimpse of regularity (although it is partial) in the order by which the building compositions change and in the order of viewing the scrolls. Emaki are viewed using the unique method of looking at the sections that are unrolled in order. It is thought that artists did not just depict buildings in a typical fashion, but intentionally repeated character placements and compositions to create a visual flow for the viewer. Contemporary viewers were limited to members of the noble class, and this culture of visual experience was cultivated to satisfy their needs.

2.5D printing system, Mofrel, is a new technology developed by Casio Computer Co. Ltd. in Japan. Roughly describing, it is an ink-jet color printer with a unique capability to generate swelling on the printer sheet. As the height of the swelling can be controlled, this technology is called 2.5D printing. It requires special printer sheet of a three layer structure. The height of swells over the sheet is controlled by a grey scale image printed on the back side of the sheet. Blacker regions produce higher swells while whiter regions produce lower swells. This grey scale ‘heating patterns’ are not generally available and manually generated by experts. In this study we propose a method to automatically generate heating patterns for 2.5D printing of topographic contour maps. We first generate a height field corresponding to the input contour map then convert it to the grey scale image to be used as a heating pattern. Our method is based on well-known Poisson image editing approach with which the height field can be computed by solving the Poisson equation with a gradient field of the height field. We propose three different estimation methods of the gradient field. The computed height field is then converted to a heating pattern. We developed a prototype software based on this approach and conducted experiments to evaluate the computed height fields and those of the actual printed sheet.

This paper focus on the geometrical application and discussion of robotics in the field of workspace. Workspace is referred to as the space which robotic arms can achieve with their own physical limitation. In this paper, a detailed geometrical and algebraic method is presented to analyze workspace curves for generalized 4-cable planar 3-degree-of-freedom cable-driven parallel mechanisms based on the antipodal theorem. In addition, this antipodal theorem is described by Voglewede as planar cable-driven parallel mechanisms are in force-closure condition if and only if the line p1p2 is completely surrounded by two sectors formed by two pairs of lines along each cable. The algebraic expression of workspace curves is deduced, which demonstrates that these curves are conics curves or straight lines (degenerated cases). Furthermore, quadratic features of these conics curves (i.e. ellipse, parabola and hyperbola) are discussed with various simulation cases. Based on the results of case study, the type of quadratic curves of this cable-driven mechanism is dependent on the determinant of conic matrix of curve expression. This paper also shows that the static workspace curves of planar cable-driven parallel mechanism relies on the structural parameters like the installation positions of cables.

The mainly content of this thesis is to solve the problem of “getting the smallest Sphere which is tangent to non-parallel unlimited skew lines in general positions”, by using AutoCAD and MATLAB software. The AutoCAD secondary development interface VBA (Visual Basic For Application) and other interfaces which provided by MATLAB are used to realize the visualized solution of the problem. Firstly, using VBA in AutoCAD to create a user interface which will be given the initial conditions recorded in the program. Secondly, the calculation is carried out in MATLAB and the results are retuned to VBA. Finally, the graphics is generated from VBA program and displayed in the window of AutoCAD.

Graphic disciplines include, besides Descriptive Geometry, Engineering Graphics and Computer Graphics. Engineering graphics, as a part of the course, contain material on the base of design and image parts and assemblies. The course of Computer Graphics under different names is a discipline that teaches students the computer graphics technology used in the future professional activities of students. The following professional activity needs dictate the purpose, content and approach to teaching graphic disciplines. Features of graphic courses for students of Institute of Petroleum Engineering and Institute of Mechanical Engineering (Ivano-Frankivsk National Technical University of Oil and Gas) are presented in the article and conducted courses comparison.

We are practicing Monozukuri education focusing on practical fields based on the subjects of mechanical engineering, in the Department of Products Design, at the College of Industrial Technology. Students can learn not only theoretical learning but also subjects related to practical training such as processing, product design, and design. Karakuri doll production, which is one of the themes of exercise, is reproduction of Karakuri doll depicted in the illustrated “Karakuri Zui” (1796), the guide to mechanical devices from the Edo Period. “Karakuri Zui” is an enlightenment book of the machine technology and can read in National Diet Library, and Karakuri doll and Karakuri clock are listed. In graduation research, students deepen the knowledge necessary for Karakuri doll production from Karakuri Zui and other literature, determine Karakuri doll that production to. Karakuri doll is a tea carrying doll that students decided to produce. It approaches guests carrying a cup of tea and clears away the empty teacup. Students plan Karakuri doll using 2-Dimension and 3-Dimension CAD software. In 2-Dimension CAD software, data for laser cutter is created, and in 3-Dimension CAD software, assemblies are checked for errors by 3D assembly. Figure 1 shows plan Karakuri doll by 2-Dimension and 3-Dimension CAD software. Students produced Karakuri doll using various tools such as laser cutters and lathes. Through Karakuri doll production, students were able to acquire various knowledge about Monozukuri. In this paper, we report on Monozukuri education in Karakuri doll production using these methods.Fig. 1.Karakuri doll production

This paper will describe a 3D dataset processing system. The medical software programs attached to older ultrasound machines are usually restricted to the sagittal, coronal and transverse planes. We will describe a new system which is capable of handling cutting planes of arbitrary angles. Our aim is to produce algorithms that yield features of volumes of interest. We will introduce methods for speeding up these algorithms by applying multi thread and SIMD techniques on the side of the CPU, and using OpenCL [1] and (fragment [2] or compute) shaders on the side of the GPU [3].

The Constructive Solid Geometry (CSG) allows modelers to create models by using Boolean operations to combine different types of basic solids. CSG has been adopted by lots of numerical simulation codes as geometric description. In the research of reactor numerical simulation, Monte Carlo (MC) is a common method for neutronics analysis, which needs to calculate the intersections between the random flight paths of neutrons and the geometry. A lot of widely used MC codes (such as Geant4, MCNP) use CSG to describe geometry. The prerequisite to run MC code is to do geometric modeling, which however in many MC codes, is finished by manually writing text files, it is very hard to view the model and it is inefficient to build. In this work, a MC modeling tool (JLAMT) based on UG software is used to build the benchmark model. The tool supplies geometric modeling functions, physical parameter setting functions, and other assistant tools. With a flexible GUI, it helps users to achieve quick modeling.

When the plane truncates the right circular cone, a circle, an ellipse, a parabola, a hyperbolic curve, and a straight line are generated. In particular, when the angle between the truncated plane and the axis is larger than the top angle of the cone, the curve obtained by the truncated cone: circle and ellipse. This cutting method is an important way that it can make connection of pipe segments in the actual project. It is very important to analyze the laws of this cutting method. When making all the truncated planes pass through a specific point, the trajectory of these Elliptic short axis endpoints is on a parabola. In water Conservancy projects, it is often necessary to use a curved pipe to connect two pipes of different diameters. This curved pipe is a warp bend. The warp bending pipe, also known as the spherical shift surface, the horn surface, and the radial bending pipe, is an unexpandable surface. In water Conservancy projects, in the hydraulic transition section, which is rounded by Square, it is also constructed with circular curved surfaces.

A geodesic path can be computed when the locations of two points on surface are fixed. It is an attractive research subject to make this method more simple, intuitive, and universal. First, the surface is discretized into a point cloud, and the line connecting the two known points is represented by points too. According to the sufficient conditions of geodesic, the principal normal vector of the geodesic at every point coincides with the normal vector of surface at that point, and the points on the line are projected onto the surface to form the curve C1 which is composed of discrete points. The geodesic path is also the shortest one between the two known points on the surface. Connect the two known points to a point picked on curve C1 into two lines respectively, and then the two lines are orthographically projected on the surface into two curves. For every point on curve C1, two projected curves can be obtained by the method above. If the sum of the lengths of the two projected curves is minimal, this point is supposed on the geodesic. Those points are computed by this method (called OPA), after, they are smoothly connected into a curve, which is the geodesic. According the analysis above, an algorithm for computing points on the geodesic is designed. The correctness of the geodesic computed by this method can be verified by the graphical of Frenet frame. The advantages of the point clouds method of digital experiment proposed in this paper are as follows: not being limited by surface shape, intuitive, precision can be controlled, stable and reliable.