Minimal energy surfaces using parametric splines

被引：32

作者：

Fasshauer, GE ^{[1
]}

Schumaker, LL ^{[1
]}

机构：

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

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1996年 / 13卷 / 01期

基金：

美国国家科学基金会;

关键词：

minimal energy surfaces; parametric splines; generalized triangulations; interpolation; filling holes; crowning;

D O I：

10.1016/0167-8396(95)00006-2

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We explore the construction of parametric surfaces which interpolate prescribed 3D scattered data using spaces of parametric splines defined on a 2D triangulation. The method is based on minimizing certain natural energy expressions. Several examples involving Ailing holes and crowning surfaces are presented, and the role of the triangulation as a parameter is explored. The problem of creating closed surfaces is also addressed. This requires introducing spaces of splines on certain generalized triangulations.

引用

页码：45 / 79

页数：35

共 64 条

[1] ON THE DIMENSION OF BIVARIATE SPLINE SPACES OF SMOOTHNESS-R AND DEGREE D = 3R + 1
ALFELD, P
SCHUMAKER, LL
[J]. NUMERISCHE MATHEMATIK, 1990, 57 (6-7) : 651 - 661
[2] AN EXPLICIT BASIS FOR C1 QUARTIC BIVARIATE SPLINES
ALFELD, P
PIPER, B
SCHUMAKER, LL
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) : 891 - 911
[3] THE GENERIC DIMENSION OF THE SPACE OF C1 SPLINES OF DEGREE D-GREATER-THAN-OR-EQUAL-TO-8 ON TETRAHEDRAL DECOMPOSITIONS
ALFELD, P
SCHUMAKER, LL
WHITELEY, W
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1993, 30 (03) : 889 - 920
[4] Alfeld P., 1984, Computer-Aided Geometric Design, V1, P169, DOI 10.1016/0167-8396(84)90029-3
[5] ALFELD P, 1984, 2707 MRC U WISC MAD
[6] [Anonymous], GEOMETRIC MODELING
[7] CELNIKER G, 1991, COMP GRAPH, V25, P257, DOI 10.1145/127719.122746
[8] COONS S, 1964, SURFACES COMPUTER AI
[9] de Boor C, 1987, GEOMETRIC MODELING A, P131
[10] DEROSE T, 1992, MATH METHODS COMPUTE, V2, P185

← 1 2 3 4 5 6 7 →