Shape analysis on Lie groups with applications in computer animation

Elena  Celledoni; Markus  Eslitzbichler; Alexander  Schmeding

doi:10.3934/jgm.2016008

Article Contents

2016, Volume 8, Issue 3: 273-304. Doi: 10.3934/jgm.2016008

This issue Previous Article Neighboring extremal optimal control for mechanical systems on Riemannian manifolds Next Article The projective symplectic geometry of higher order variational problems: Minimality conditions

Shape analysis on Lie groups with applications in computer animation

1.
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim

Received: June 2015

Revised: May 2016

Published: September 2016

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Abstract

Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher dimensional curves, surfaces, activities, character motions and many other objects.
In this paper, we develop a framework for shape analysis of curves in Lie groups for problems of computer animations. In particular, we will use these methods to find cyclic approximations of non-cyclic character animations and interpolate between existing animations to generate new ones.

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Mathematics Subject Classification: 65D18, 58J90, 58D10, 49Q10.

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