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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SIGGRAPH. , 2011. Discretization of asymptotic line parametrizations using hyperboloid surface patches. 3508. , AND RUBIO, W. 2008. Optimising positioning of the axis of a milling cutter on an offset surface by geometric error minimisation. Int. 1. Adv. Manufacturing Technology 37,861-871. , AND RAVANI, B. 2008. Cylindrical milling of ruled surfaces. Int. 1. Adv. Manufacturing Technology 38, 649-656. WALLNER, 1. 2012. On the semidiscrete differential geometry of A-surfaces and K-surfaces. 1. Geometry 103, 161-176.

P. Feldmann, J. Mason, R. J. 2 Geometry The 'neckline', defined in elevation as the transition point between the lower and upper arcs, is also the transition point in logic between the spiralling, algorithmic base and the geometrically defined tower head. Above this point, the tower transforms from a circle into an elongated elliptical shape to compress through the two cable car travel paths. This profile is defined by the top arc in the long section and a tangent straight line in the short section.

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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