Modeling with C Quintic A-patches

We present an e cient algorithm to construct C smooth meshes of quintic A-patches that interpolate or approximate the vertices of a given triangulated polyhedron P. An A-patch is a smooth and functional zero-contour patch of a trivariate polynomial in Bernstein-B ezier (BB) form de ned within a tetrahedron. A simplicial hull is constructed based on P. A quintic A-patch is then constructed within each tetrahedron of so that the piecewise C algebraic surface interpolates or approximates the vertices of P with given C data. We guarantee that the algebraic surface is smooth and functional, namely, fully connected and free of singularity, unwanted branches.