Animation manifolds for representing topological alteration

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.