Transfinite mean value interpolation

被引：49

作者：

Dyken, Christopher ^{[1
]}

Floater, Michael S. ^{[1
]}

机构：

[1] Univ Oslo, IFI CMA, Oslo, Norway

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2009年 / 26卷 / 01期

关键词：

Transfinite interpolation; Hermite interpolation; Mean value coordinates; CONVEX; CONSTRUCTION;

D O I：

10.1016/j.cagd.2007.12.003

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpolation when f is continuous. Then, by dedving the normal derivative of the interpolant and of a mean value weight function, we construct a transfinite Hermite interpolant and discuss Various applications. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：117 / 134

页数：18

共 22 条

[1] BELYAEV A, 2006, EUR S GEOM PROC, P89
[2] Blum H., 1967, MODELS PERCEPTION SP
[3] Barycentric rational interpolation with no poles and high rates of approximation
Floater, Michael S.
Hormann, Kai
[J]. NUMERISCHE MATHEMATIK, 2007, 107 (02) : 315 - 331
[4] A general construction of barycentric coordinates over convex polygons
Floater, MS
Hormann, K
Kós, G
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2006, 24 (1-4) : 311 - 331
[5] Mean value coordinates in 3D
Floater, MS
Kós, G
Reimers, M
[J]. COMPUTER AIDED GEOMETRIC DESIGN, 2005, 22 (07) : 623 - 631
[6] Mean value coordinates
Floater, MS
[J]. COMPUTER AIDED GEOMETRIC DESIGN, 2003, 20 (01) : 19 - 27
[7] PSEUDO-HARMONIC INTERPOLATION ON CONVEX DOMAINS
GORDON, WJ
WIXOM, JA
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1974, 11 (05) : 909 - 933
[8] Höllig K, 2001, SIAM J NUMER ANAL, V39, P442, DOI 10.1137/S0036142900373208
[9] HOLLIG K, 2003, FRONT APP M, P1
[10] Mean value coordinates for arbitrary planar polygons
Hormann, Kai
Floater, Michael S.
[J]. ACM TRANSACTIONS ON GRAPHICS, 2006, 25 (04): : 1424 - 1441

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