Computing geodesics on triangular meshes

被引：71

作者：

Martínez, D

Velho, L

Carvalho, PC

机构：

[1] IMPA, Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, RJ, Brazil

[2] ICIMAF Inst Cibernet Matemat & Fis, Havana, Cuba

来源：

COMPUTERS & GRAPHICS-UK | 2005年 / 29卷 / 05期

关键词：

shortest geodesic; manifold triangulation; curve evolution;

D O I：

10.1016/j.cag.2005.08.003

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian's Fast Marching Method and Polthier's straightest geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and non-convex surfaces. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：667 / 675

页数：9

共 13 条

[1]

Aleksandrov A.D., 1967, TRANSLATION MATH MON, V15

[2]

CHEN JD, 1990, PROCEEDINGS OF THE SIXTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY, P360, DOI 10.1145/98524.98601

[3]

do Carmo P., 1976, Differential Geometry of Curves and Surfaces

[4]

Floater M, 2002, TUTORIALS ON MULTIRESOLUTION IN GEOMETRIC MODELLING, P287

[5]

Kapoor S., 1999, Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, P770, DOI 10.1145/301250.301449

[6] Computing geodesic paths on manifolds [J].

Kimmel, R ;

Sethian, JA .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1998, 95 (15) :8431-8435

[7]

MARTINEZ D, UNPUB PROOF CONVERGE

[8] THE DISCRETE GEODESIC PROBLEM [J].

MITCHELL, JSB ;

MOUNT, DM ;

PAPADIMITRIOU, CH .

SIAM JOURNAL ON COMPUTING, 1987, 16 (04) :647-668

[9]

Polthier K., 1999, DATA VISUALIZATION

[10]

Polthier Konrad, 1998, Mathematical Visualization: Algorithms, Applications and Numerics, P135

← 1 2 →