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Quad/Triangle Subdivision
Author(s) -
Stam Jos,
Loop Charles
Publication year - 2003
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.t01-2-00647
Subject(s) - subdivision surface , subdivision , polygon mesh , quadrilateral , triangle mesh , curvature , computer science , boundary (topology) , bounded function , mathematics , computer graphics , volume mesh , computer graphics (images) , mean curvature , generalization , surface (topology) , mesh generation , geometry , finite element method , mathematical analysis , physics , history , thermodynamics , archaeology
In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad‐only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull‐Clark and Loop subdivision algorithms. We show that our surfaces areC1everywhere and provide a proof that it is impossible to construct such aC2scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples.ACM CSS: I.3.5 Computer Graphics— Curve, surface, solid, and object representations