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## Über dieses Buch

This book explores the extremely modular systems that meet two criteria: they allow the creation of structurally sound free-form structures, and they are comprised of as few types of modules as possible. Divided into two parts, it presents Pipe-Z (PZ) and Truss-Z (TZ) systems. PZ is more fundamental and forms spatial mathematical knots by assembling one type of unit (PZM). The shape of PZ is controlled by relative twists of a sequence of congruent PZMs. TZ 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 combination of both).

## Inhaltsverzeichnis

### Chapter 1. The Skin of a Building

Abstract
This chapter describes the main functions of Building Envelopes, particularly in the context of daylighting (including the role of the outside view, smart windows, etc.). The functions of Building Envelope are compared with organic skin. Finally, an example of a relatively successful integration of adaptivity and aesthetics in the building of the Arab World Institute is presented.
Machi Zawidzki

### Chapter 2. Cellular Automaton-Based Shading System (CASS)

Abstract
This chapter collects the findings of the research on the cellular automaton-based shading systems (CASS) for building envelopes. CASS is based on congruent modular units, thus it has the potential of being inexpensive and robust. Two approaches for the realization of CASS are presented: based on the liquid crystal technology, and based on the rotation of polarized film elements. Several optimization methods of CASS are presented. The optimization criteria include: the “grayness” monotonicity, and cellular automaton (CA) pattern distribution error which represent: the level of control over the CA pattern, and its uniformity over entire array of cells, respectively. The robustness of CASS for various types of failure is discussed.
Machi Zawidzki

### Chapter 3. Polarized Film Shading System in Regular Grids (PFSS)

Abstract
Although the prototype of CASS documented in Ref. [13] has been based on liquid crystal (LC) technology, the original concept was imagined as an opto-mechanical system of square plates made of polarized glass [9]. Materialization of the reduced-scale prototype with prefabricated LC elements has been the most straightforward. The size of the shading element in the prototype was approx. $$12\times 12$$ mm, which is by a range of magnitude smaller than intended final device. Thus in the full-scale prototype, this method probably would not be the most economical choice. The technology constantly evolves and high-tech solutions tend to become more affordable. Nevertheless, LC elements remain relatively expensive both in terms of: fabrication and running cost. LC available on the market requires approx. 5 $$W\over m^{2}$$ of continuous power in the activated state [8]. Furthermore, according to [2] the transmittance modulation for commercial LC windows has been found unsatisfactory. Moreover, due to instability for UV radiation, LC windows have not been found appropriate for long-term building façade applications. This chapter further investigates the original method, where shading elements are comprised of two polygonal sheets of normally white polarized film.
Machi Zawidzki

### Chapter 4. Two-Dimensional Triangular Cellular Automata on Surfaces

Abstract
As mentioned in the previous chapter, it seems substantially easier to control the state of a regular-polygon surface with one- than two-dimensional CAs. However, 2D CAs also offer certain advantages which are investigated here.
Machi Zawidzki

### Chapter 5. Cellular Automaton-Based Shading System Prototypes

Abstract
The research on Cellular Automata (CA) has already commenced in the first half of the twentieth century. However, since then only a few devices have been built based or inspired by them. Nearly a decade ago the concept of Cellular Automaton-based Shading System (CASS) for dynamic control of a Building Envelope has been introduced. This chapter presents two alternative approaches for the physical implementation of CASS based on 1. Liquid Crystal Display (LCD) technology; 2. Relative rotation of elements made of polarized film, so-called Polarized Film Shading System (PFSS).
Machi Zawidzki

### Chapter 6. Static Solar Shading of a Free-Form Building with Shade-Z

Abstract
Proper positioning and sizing of windows are essential for supplying sufficient amounts of daylight into a building. On the other hand, windows are often the source of excessive insolation causing glare and overheating, which have negative impact on the energy performance of a building, and most importantly - on the comfort and well-being of users. Development of tools for simulation of daylight and optimization of shading has already commenced in the 1970s. Nevertheless, none of the available design tools can naturally handle free-form apertures in a free-form surface (FFS) of a building envelope. This chapter presents Shade-Z, SZ for short, an intuitive design aid. SZ is intended for architects to be used at any, especially the early stages of design to ensure proper shading from undesirable insolation. The input for SZ are: the geometrical data of given FFS, geographical location, time-zone, required annual periods and hours for both: allowing and blocking direct sunbeams. SZ automatically detects the apertures and generates the geometry of static shading. The algorithm is explained and illustrated with an example of a free-form aperture in FFS located in Warsaw, Poland.
Machi Zawidzki

### Backmatter

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