A Class of $C^1$ Discrete Interpolants over Tetrahedra

Abstract

Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of $C^1$ discrete tetrahedral interpolants with only $C^1$ data required. As special cases of the class characterized, we give two $C^1$ discrete tetrahedral interpolants which have concise expressions.