Shortening three-dimensional curves via two-dimensional flows

R. Kimmel; G. Sapiro

doi:10.1016/0898-1221(94)00228-D

Shortening three-dimensional curves via two-dimensional flows

R. Kimmel, G. Sapiro

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In this paper, a curve evolution approach for the computation of geodesic curves on 3D surfaces is presented. The algorithm is based on deforming, via the curve shortening flow, an arbitrary initial curve ending at two given surface points. The 3D curve shortening flow is first transformed into an equivalent 2D one. This 2D flow is implemented, using an efficient numerical algorithm for curve evolution with fixed end points.

Original language	English (US)
Pages (from-to)	49-62
Number of pages	14
Journal	Computers and Mathematics with Applications
Volume	29
Issue number	3
DOIs	https://doi.org/10.1016/0898-1221(94)00228-D
State	Published - Feb 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Keywords

Curve shortening flow
Geodesic curvature
Geodesic curve
Numerical implementation

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10.1016/0898-1221(94)00228-D

Cite this

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abstract = "In this paper, a curve evolution approach for the computation of geodesic curves on 3D surfaces is presented. The algorithm is based on deforming, via the curve shortening flow, an arbitrary initial curve ending at two given surface points. The 3D curve shortening flow is first transformed into an equivalent 2D one. This 2D flow is implemented, using an efficient numerical algorithm for curve evolution with fixed end points.",

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AU - Sapiro, G.

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AB - In this paper, a curve evolution approach for the computation of geodesic curves on 3D surfaces is presented. The algorithm is based on deforming, via the curve shortening flow, an arbitrary initial curve ending at two given surface points. The 3D curve shortening flow is first transformed into an equivalent 2D one. This 2D flow is implemented, using an efficient numerical algorithm for curve evolution with fixed end points.

KW - Curve shortening flow

KW - Geodesic curvature

KW - Geodesic curve

KW - Numerical implementation

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ER -

Shortening three-dimensional curves via two-dimensional flows

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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