A Degree Estimate for PolynomialSubdivision Surfaces of Higher RegularitybyUlrich

Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. However, in contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents an estimate for piecewise polynomial subdivision surfaces by pointing out that curvature continuity is possible only if the bi-degree d of the patches satisses d 2k + 2, where k is the order of smoothness on the regular part of the surface. This result applies to any stationary or non-stationary scheme consisting of masks of arbitrary size provided that some generic symmetry and regularity assumptions are fulllled. Abstract Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. However, in contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents an estimate for piecewise polynomial subdivision surfaces by pointing out that curvature continuity is possible only if the bi-degree d of the patches satisses d 2k + 2, where k is the order of smoothness on the regular part of the surface. This result applies to any stationary or non-stationary scheme consisting of masks of arbitrary size provided that some generic symmetry and regularity assumptions are fulllled.