%0 Journal Article %T An Approximating-Interpolatory Subdivision Scheme. %+ Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i) %A Boumzaid, Yacine %A Lanquetin, Sandrine %A Neveu, Marc %A Destelle, François %< avec comité de lecture %@ 1311-8080 %J International Journal of Pure and Applied Mathematics %I Academic Publishing Ltd %V 71 %N 1 %P 129-147 %8 2011 %D 2011 %K Subdivision %K Polynomial generation %K Quad/triangle Subdivision %K Quasi-interpolants %Z Numerical analysis, Computer science %Z Computer Science [cs]/Graphics [cs.GR]Journal articles %X 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. %G English %2 https://u-bourgogne.hal.science/hal-00639051/document %2 https://u-bourgogne.hal.science/hal-00639051/file/An_Approximating-Interpolatory_subdivision_scheme.pdf %L hal-00639051 %U https://u-bourgogne.hal.science/hal-00639051 %~ UNIV-BOURGOGNE %~ CNRS %~ ENSAM %~ LE2I %~ AGREENIUM %~ LIB_UB %~ LIB_MODGEOM %~ ARTS-ET-METIERS-SCIENCES-ET-TECHNOLOGIES %~ HESAM %~ HESAM-ENSAM %~ INSTITUT-AGRO