Interpolating Rational Splines in Three Dimensional Space

Abstract:

      Let a polyhedron in three dimensional space be decomposed into tetrahedral cells by a certain partition. In this paper efforts are made on assigning appropriate nodes along the edges of every tetrahedron and characterizing interpolation data that determine a unique rational function of type (1,1), which is nonsingular in the corresponding tetrahedron. By constructing suitable basis functions and restricting the interpolation data, necessary and sufficient conditions for the existence of rational splines with C⁰ as well as C¹ smoo thness are fo rmulated respectively.