Department of Computer Science and Technology

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.


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.

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BibTeX record

  author =	 {Southern, Richard},
  title = 	 {{Animation manifolds for representing topological
  year = 	 2008,
  month = 	 jul,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  number = 	 {UCAM-CL-TR-723}