Short note: Fast geodesics computation with the phase flow method

Authors:
Lexing Ying;Emmanuel J. Candès
Affiliations:
Applied and Computational Mathematics, California Institute of Technology, Caltech, MC 217-50, Pasadena, CA 91125, United States;Applied and Computational Mathematics, California Institute of Technology, Caltech, MC 217-50, Pasadena, CA 91125, United States
Venue:
Journal of Computational Physics
Year:
2006

Citing 6
Cited 2

The discrete geodesic problem

SIAM Journal on Computing
Topology matching for fully automatic similarity estimation of 3D shapes

Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Geomodeling

Geomodeling
Fast exact and approximate geodesics on meshes

ACM SIGGRAPH 2005 Papers
The phase flow method

Journal of Computational Physics
A fast phase space method for computing creeping rays

Journal of Computational Physics

An Eulerian approach for computing the finite time Lyapunov exponent

Journal of Computational Physics
An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems

Journal of Computational Physics

Quantified Score

Hi-index	31.46

Visualization

Abstract

This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface. The idea is to apply the recently developed phase flow method [L. Ying, E.J. Candes, The phase flow method, J. Comput. Phys., to appear], an efficient and accurate technique for constructing phase maps for nonlinear ordinary differential equations on invariant manifolds, which are here the unit tangent bundles of the surfaces under study. We show how to rapidly construct the whole geodesic flow map which then allows computing any geodesic by straightforward local interpolation, an operation with constant complexity. A few numerical experiments complement our study and demonstrate the effectiveness of our approach.