THE GENERIC DIMENSION OF THE SPACE OF C1 SPLINES OF DEGREE D-GREATER-THAN-OR-EQUAL-TO-8 ON TETRAHEDRAL DECOMPOSITIONS

被引：30

作者：

ALFELD, P

SCHUMAKER, LL

WHITELEY, W

机构：

[1] VANDERBILT UNIV,DEPT MATH,NASHVILLE,TN 37240

[2] YORK UNIV,DEPT MATH & STAT,N YORK M3J 1P3,ONTARIO,CANADA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1993年 / 30卷 / 03期

关键词：

MULTIVARIATE SPLINES; PIECEWISE POLYNOMIAL FUNCTIONS; TRIANGULATIONS; PROJECTION; EDGE CONTRACTING; GENERIC DIMENSIONS;

D O I：

10.1137/0730047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers the linear space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain which has been partitioned into tetrahedra. Combining Bernstein-Bezier methods and combinatorial and geometric techniques from rigidity theory, this paper gives an explicit expression for the generic dimension of this space for sufficiently large polynomial degrees (d greater-than-or-equal-to 8). This is the first general dimension statement of its kind.

引用

页码：889 / 920

页数：32

共 10 条

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