Parametric triangular Bézier surface interpolation with approximate continuity

Abstract

A piecewise quintic interpolation scheme with approximate G1 continuity is presented. For a given triangular mesh of arbitrary topology, one quintic triangular Bézier patch is constructed for each data triangle. Although the resulting surface has G1 continuity at the data vertices, we only require approximate G1 continuity along the patch boundaries so as to lower the patch degree. To reduce the normal discontinuity along boundaries, neighbouring patches are adjusted to have identical normals at the middle point of their common boundary. In most cases, the surfaces generated by this scheme have the same level of visual smoothness compared to an existing sextic G1 continuous interpolation scheme. Further, using the new boundary construction method presented in this paper, better shape quality is observed for sparse data sets than the surfaces of the original G1 continuous scheme, upon which the new scheme is based.