Approximate G1 Cubic Surfaces for Data Approximation

This paper presents a piecewise cubic approximation method with approximate G1 continuity. For a given triangular mesh of points with arbitrary topology, one cubic triangular Bézier patch surface is constructed. The resulting surfaces have G1 continuity at the vertex points, but only requires approximate G1 continuity along the macro-patch boundaries so as to lower the patch degree. While our scheme cannot generate the surfaces in as high quality as Loop’s sextic scheme, they are of half the polynomial degree, and of far better shape quality than the results of interpolating split domain schemes.