Generating genus-n-to-m mesh morphing using spherical parameterization

Abstract

Surface parameterization is a fundamental tool in computer graphics and benefits many applications such as texture mapping, morphing, and re-meshing. Many spherical parameterization schemes with very nice properties have been proposed and widely used in the past. However, it is well known that the spherical parameterization is limited to genus-0 models. In this paper, we first propose a novel framework to extend spherical parameterization for handling a genus-n surface. In this framework, we represent a surface S of arbitrary genus by a positive mesh O and several negative meshes N i. Each negative surface is used to represent a hole. A positive surface O is obtained by removing all holes in the original surface S. Then, both positive and negative meshes are genus-0 and can be spherically parameterized, respectively. To compute S, we can use a Boolean difference operation to subtract negative N i from a positive O. Next, we apply this novel framework to generate genus-n-to-m mesh morphing application without restriction of n = m. Finally, there are many interesting non-genus-0 mesh morphing sequences generated. Copyright © 2006 John Wiley & Sons, Ltd.