Triangular G1 interpolation by 4-splitting domain triangles

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructing C-consistent boundary curves. Piecewise C boundary curves and a regular 4-split of the domain triangle make shape parameters available for controlling locally the boundary curves. A small number of free inner control points can be chosen for some additional local shape e ects.