Shape Analysis on Lie Groups with Applications in Computer Animation

TL;DR

This paper develops a framework for shape analysis of curves in Lie groups, enabling applications in computer animation such as cyclic approximation and interpolation of character motions.

Contribution

It introduces a novel shape analysis framework for curves in Lie groups tailored for computer animation applications.

Findings

Successfully approximates non-cyclic animations with cyclic ones

Interpolates between animations to generate new motion sequences

Provides a mathematical foundation for shape analysis in Lie groups

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.