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The New Horizons of Oblique Axonometry

The Geometry of the Drawing Geometric Experimentation

  • 2025
  • Book
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About this book

This book offers a structured and original exploration of oblique axonometry as a complete and autonomous system of spatial representation. Through a progressive sequence of theoretical insights and geometric constructions, it provides a methodological approach to drawing that privileges reasoning over automation. Starting from the fundamentals of oblique parallel projection, the book guides the reader through the restitution of coordinate systems, the interpretation of lines and planes, and the construction of complex geometric entities—including polyhedra, ruled surfaces, helicoids, and toroids.

Far from merely illustrating procedures, the author frames axonometry as a synthetic language capable of expressing space with clarity and intellectual depth. Special attention is given to the geometric properties of forms, their projection behaviors, and the relationships between spatial and figurative elements.

Designed for students, educators, and professionals in architecture, engineering, and design, the book aims to renew interest in descriptive geometry and stimulate critical thinking through spatial reasoning. The examples and exercises proposed support autonomous learning and conceptual mastery, while offering a perspective that is at once rigorous and creatively open. This book provides a valuable resource for those interested in rediscovering the expressive and analytical potential of the drawing line.

Table of Contents

Frontmatter
Chapter 1. Oblique Parallel Projection
Abstract
This chapter introduces the foundational principles of oblique axonometric projection, establishing its relationship to orthogonal axonometry while emphasizing its autonomy as a complete system of representation. The theoretical framework is developed through spatial reasoning, without reliance on imagery, guiding the reader to a deeper conceptual understanding of projection geometry. Definitions of spatial elements and their infinite and relative properties are explored, preparing the reader for the practical and intellectual challenges of oblique drawing. The aim is to develop conscious, methodical control of geometric representation, overcoming intuitive but imprecise approaches to descriptive geometry.
Laura Inzerillo
Chapter 2. Geometry of the Drawing in Oblique Axonometry
Abstract
This chapter delves into the geometric mechanics underlying oblique axonometric projections. It focuses on the projection and restitution of coordinate systems, starting from an oblique projection of the standard triplet (O, x, y, z) onto a picture plane. Through analytical constructions and homological relationships, the chapter illustrates how to determine obliquity, evaluate projections of geometric elements, and calculate distortions. Emphasis is placed on the role of geometric reasoning in defining projection parameters and on how variations in angles and positions affect the resulting image. The chapter lays the groundwork for consistent and reproducible drawing practices in oblique axonometry.
Laura Inzerillo
Chapter 3. Oblique Axonometry: Coordinated Plane Parallel to π
Abstract
This chapter explores cases in which the projection plane p is parallel to one of the coordinate planes, particularly focusing on xy. It examines the simplifications and visual effects produced by this condition and offers a detailed analysis of the representation and reading of points, lines, and planes. Through geometric constructions, the text presents how to identify traces, intersections, and projections of spatial elements under specific obliquity conditions. Practical exercises guide the reader through the interpretation of drawing distortions and projection-induced transformations. The chapter also highlights the challenges of interpreting spatial data in a flat image.
Laura Inzerillo
Chapter 4. Volumes in Oblique Axonometry
Abstract
This chapter extends oblique axonometric techniques to the representation of complex three-dimensional solids. Starting with polyhedra and progressing to ruled and curved surfaces—such as helicoids, quadrics, and toroids—it presents methods for accurate geometric construction and projection. The chapter emphasizes the importance of visual reasoning and proportional relationships in creating readable, accurate, and scalable images. It also addresses aggregate forms and symmetry operations. Special attention is given to the implications of projection direction on the deformation and readability of the volumes. This section consolidates and applies the concepts introduced in earlier chapters to volumetric geometry.
Laura Inzerillo
Backmatter
Title
The New Horizons of Oblique Axonometry
Author
Laura Inzerillo
Copyright Year
2025
Electronic ISBN
978-3-032-07475-1
Print ISBN
978-3-032-07474-4
DOI
https://doi.org/10.1007/978-3-032-07475-1

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