Parametric Cubic Spline Interpolating Surfaces for Arbitrary Polygonal Meshes

An innovative and efficient algorithm was established for generating a G1 parametric bicubic spline interpolation surface (PACSIS) for any polygonal mesh. The resulting G1 surface interpolates all vertices of the quads; and the G1 smoothness was guaranteed by the special creation of new control points for each quad so that all tangent planes at any vertex match. The algorithm was demonstrated by a variety of PLY files representing different polygonal meshes. There will be more applications of PACSIS to areas such as signal and image processing, animation, data science, feature representation, mesh rendering, visualization, as well as computer graphics.