3D geometric metamorphosis based on harmonic map

Abstract

Recently, animations with deforming objects are frequently used in various computer graphics applications. Metamorphosis (or morphing) of three dimensional objects can realize a shape transformation between two or more existing objects. We present a new algorithm for 3D geometric metamorphosis between two objects based on the harmonic map. Our algorithm is applicable for arbitrary polyhedra that are homeomorphic to the three dimensional sphere or the two dimensional disk. In our algorithm, each of the two 3D objects is first embedded to the circular disk on the plane. This embedded model has the same graph structure as its 3D objects. By overlapping those two embedded models, we can establish a correspondence between the two objects. Using this correspondence, intermediate objects between two objects are easily generated. The user only specifies a boundary loop on an object and a vertex on that boundary which control the interpolation.