An Approximating-Interpolatory Subdivision Scheme.

Abstract : In the last decade, study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control mesh consisting of both quads and triangles and produces ner and ner meshes with quads and triangles (Fig. 1). Design- ers often want to model certain regions with quad meshes and others with triangle meshes to get better visual qual- ity of subdivision surfaces. Smoothness analysis tools exist for regular quad/triangle vertices. Moreover C1 and C2 quad/triangle schemes (for regular vertices) have been con- structed. But to our knowledge, there are no quad/triangle schemes that uni es approximating and interpolatory sub- division schemes. In this paper we introduce a new subdivision operator that uni es triangular and quadrilateral subdivision schemes. Our new scheme is a generalization of the well known Catmull- Clark and Butterfly subdivision algorithms. We show that in the regular case along the quad/triangle boundary where vertices are shared by two adjacent quads and three adjacent triangles our scheme is C2 everywhere except for ordinary Butterfly where our scheme is C1.
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Submitted on : Tuesday, November 8, 2011 - 11:42:44 AM
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Yacine Boumzaid, Sandrine Lanquetin, Marc Neveu, François Destelle. An Approximating-Interpolatory Subdivision Scheme.. International Journal of Pure and Applied Mathematics, Academic Publishing Ltd, 2011, 71 (1), pp.129-147. ⟨hal-00639051⟩

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