三维空间中的有理样条插值

对三维空间某个多面体区域的四面体剖分，通过在每个四面体胞腔的棱和顶点设置适当的插值结点．本文给出了（１，１）型Ｃ⁰及Ｃ¹光滑的非奇异有理样条存在的充分必要条件．

Interpolating Rational Splines in Three Dimensional Space

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.