Download Advances in Architectural Geometry 2012 by Robert Aish, Aparajit Pratap (auth.), Lars Hesselgren, PDF

By Robert Aish, Aparajit Pratap (auth.), Lars Hesselgren, Shrikant Sharma, Johannes Wallner, Niccolo Baldassini, Philippe Bompas, Jacques Raynaud (eds.)

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Problems arose mostly in enforcing watertightness. We should remark that using a common boundary for adjacent strips will of course overcome that problem, but it will also cost valuable degrees of freedom. Figure 12: A reference surface (blue) which is an unmodified part of the Cagliari museum project by Zaha Hadid architects has been manually initialized and has subsequently been approximated with a single conoidal ruled surface (green) and with a general ruled surface (orange). The bottom row shows these three surfaces superimposed on each other in order to visualize approximation quality.

In a first step we tried to find heuristics that reduce the number of defect configurations. Generally, defects on the same row repel each other. Therefore, we placed defects on the same row in greatest possible distance. This assumption was confirmed by several numerical experiments. Further, we expected that defects on different neighboring layers also repel each other. Here, numerical experiments proved the opposite, layouts never lead to overall good configurations. Also, heuristics involving the curvature data of the surface did not lead to desired results.

Side conditions (keeping boundary curves in previously selected planes, keeping strip endpoints fixed, keeping end ruling directions fixed, ... ) are linear and thus easy to enforce as hard constraints. Figure 10 shows a result of optimization with the side condition of planar boundaries. The conoidal condition is treated in a similar way: it is easy to see that a degree (n, 1) B-spline strip defined by control points {bij }{:g,l n is conoidal if and only if all vectors biQ - bil are orthogonal to some common vector.

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