Parametric Cubic Spline Interpolating Surfaces for Arbitrary Polygonal Meshes

A fast algorithm for generating pseudo first order geometrically differentiable surfaces for arbitrary polygonal meshes by using parametric bicubic spline interpolation, to be called PACSIS, is established. It can be applied to any polygonal mesh as a quadrilateralization preprocessing can be performed if not all polygons of the given polygonal mesh are quadrilaterals. If needed, the resulting pseudo first order geometrically differentiable surface can create and provide point clouds with any desirable density based on available polygonal meshes. Various examples are demonstrated.