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Journal for Geometry and Graphics 12 (2008), No. 1, 035--052
Copyright Heldermann Verlag 2008

Subdivision Algorithms for Ruled Surfaces

Boris Odehnal
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1230 Vienna, Austria

Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algorithm combines subdivision for the striction curve with geodesic subdivision in the Euclidean unit sphere. The third method is based on the Denavit-Hartenberg-Method for serial robots. We refine the sequence of motions of the Sannia frame by means of geodesic subdivision in the group of Euclidean motions.

Keywords: Subdivision, ruled surface, striction curve, geodesic subdivision, Euclidean motion, Sannia frame.

MSC: 53A25; 65Y25, 52-xx, 68U07

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