Experimental Mathematics

Discrete periodic geodesics in a surface

Anders Linnér and Robert Renka

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Abstract

An alternative to the traditional curve-straightening flow on periodic curves in surfaces is introduced. The implementation of this flow produces periodic geodesics in minutes rather than hours. The flow is also simpler to initiate since its use of a penalty method permits initial curves that are not necessarily in the surface. Compact and noncompact examples are provided as well as examples with trivial and nontrivial free homotopy classes. The explicit curve-straightening flow on circles in Euclidian space is derived to help check the consistency of the implementations.

Article information

Source
Experiment. Math., Volume 14, Issue 2 (2005), 145-152.

Dates
First available in Project Euclid: 30 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.em/1128100127

Mathematical Reviews number (MathSciNet)
MR2169518

Zentralblatt MATH identifier
1120.53024

Subjects
Primary: 49M25: Discrete approximations 53C22: Geodesics [See also 58E10] 58E10: Applications to the theory of geodesics (problems in one independent variable) 65K10: Optimization and variational techniques [See also 49Mxx, 93B40]

Keywords
Curve-straightening elastic energy geodesic curvature periodic geodesic Sobolev gradient

Citation

Linnér, Anders; Renka, Robert. Discrete periodic geodesics in a surface. Experiment. Math. 14 (2005), no. 2, 145--152. https://projecteuclid.org/euclid.em/1128100127


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