Locally generated Hermitian C1-splines on triangular meshes

[摘要] We classify all possible local linear procedures on triangular meshes resulting in polynomial C 1 -spline functions with affinely uniform shape conditions for the basic functions at the edges, and fitting the 9 value and gradient data at the vertices of the mesh triangles. There is a unique procedure among them with shape functions and basic polynomials of degree 5 and all other admissible procedures are its perturbations with higher degree.

[学科分类] 数学（综合）

[关键词] Polynomial C 1 -spline;triangular mesh;gradient data.