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.

DOI: 10.48456/tr-723


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},
  doi = 	 {10.48456/tr-723},
  number = 	 {UCAM-CL-TR-723}