Technical reports

# Animation manifolds for representing topological alteration

**Richard Southern**

July 2008, 131 pages

This technical report is based on a dissertation submitted February 2008 by the author for the degree of Doctor of Philosophy to the University of Cambridge, Clare Hall.

## Abstract

An animation manifold encapsulates an animation sequence of surfaces contained within a higher dimensional manifold with one dimension being time. An iso–surface extracted from this structure is a frame of the animation sequence.

In this dissertation I make an argument for the use of animation manifolds as a representation of complex animation sequences. In particular animation manifolds can represent transitions between shapes with differing topological structure and polygonal density.

I introduce the animation manifold, and show how it can be constructed from a keyframe animation sequence and rendered using raytracing or graphics hardware. I then adapt three Laplacian editing frameworks to the higher dimensional context. I derive new boundary conditions for both primal and dual Laplacian methods, and present a technique to adaptively regularise the sampling of a deformed manifold after editing.

The animation manifold can be used to represent a morph sequence between surfaces of arbitrary topology. I present a novel framework for achieving this by connecting planar cross sections in a higher dimension with a new constrained Delaunay triangulation. Topological alteration is achieved by using the Voronoi skeleton, a novel structure which provides a fast medial axis approximation.

## Full text

PDF (6.7 MB)

## BibTeX record

@TechReport{UCAM-CL-TR-723, author = {Southern, Richard}, title = {{Animation manifolds for representing topological alteration}}, year = 2008, month = jul, url = {http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-723.pdf}, institution = {University of Cambridge, Computer Laboratory}, number = {UCAM-CL-TR-723} }