By Cristiano Ceccato (auth.), Cristiano Ceccato, Lars Hesselgren, Mark Pauly, Helmut Pottmann, Johannes Wallner (eds.)

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2010]. 1 Problem Specification Let F be a given input freeform surface, called reference surface, describing the shape of the design. The goal is to find a collection of panels, such that their union approximates the reference surface. Since the quality of the approximation strongly depends on the position and tangent continuity across panel boundaries, Eigensatz and coworkers identify two quality measures (see Figure 5):  divergence: quantifies the spatial gap between adjacent panels and,  kink angle: measures the jump in normal vectors between adjacent panels.

It allows implementing global design intent as well as information regarding production, detail and material. The advantages of this are apparent in the speed and accuracy by which structures could be realized in 1:1 (Figure13). g. surroundings, gravity and tectonic stress. Figure 13. no, Knippers and Helbig Advanced Engineering and Prof. Christoph Gengnagel/ TU-Berlin. References ALLEN, J. S. 1999. A Short History of 'Lamella' Roof Construction. Transactions of the Newcomen Society, Vol 71, No 1.

Figure taken from [Eigensatz et al. 2010]. 57 Eigensatz et al. While divergence is strongly related to the viability of a paneling solution, the kink angles influence the visual appearance, since they are related to reflections. Hence one can allow higher kink angles in areas not or only barely visible to an observer. 2. The intersection curves between adjacent panels are essential for the visual appearance of many designs (see Figure 2) and typically reflect the structure of the building, as they often directly relate to the underlying support structure.

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