to appear in IEEE Computer Graphics and Applications Metamorphosis of Arbitrary Triangular Meshes Takashi Kanai Materials Fabrication Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako-shi, Saitama, 351-0198, Japan. Tel: +81-48-467-9319 Fax: +81-48-462-4657 Hiromasa Suzuki Fumihiko Kimura Department of Precision Machinery Engineering, Graduate School of Engineering, The University of Tokyo, Room No.921, Engineering Building No.14, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo, 113-8656, Japan. Tel: +81-3-3812-2111 ext. 6495 Fax: +81-3-3812-8849 Abstract Recently, animations with deforming objects have been frequently used in various computer graph- ics applications. Metamorphosis (or morphing) of three-dimensional objects is one of the techniques which realizes shape transformation between two or more existing objects. In this paper, we present an efficient framework for metamorphosis between two topologically equivalent, arbitrary meshes with the control of surface correspondences by the user. The basic idea of our method is to partition meshes according to the reference shapes specified by the user, whereby vertex-to-vertex correspondences between the two meshes can be specified. Each of the partitioned meshes is embedded into a polygonal region on the plane with harmonic mapping. Those embedded meshes have the same graph structure as their original meshes. By overlapping those two embedded meshes, we can establish correspondence between them. Based on this correspondence, metamorphosis is achieved by interpolating the corresponding vertices from one mesh to the other. We demonstrate that the minimum control of surface correspondences by the user generates sophisticated results of the interpolation between two meshes. Keywords: Geometric Modeling, Metamorphosis, Surface Correspondence, Harmonic Mapping 1 Introduction Three-dimensional (3D) metamorphosis (or morphing) that establishes a smooth transition from a source object to a target object, is an active research area in computer graphics. We handle 3D geometric metamorphosis be- tween two objects which are represented as triangular meshes. The primary issue in 3D metamorphosis is to establish surface correspondence between the source and target objects, by which each point on the surface of the source object is mapped to a point on the surface of the target object [16]. Once this correspondence is es- tablished, it is possible to generate a smooth transition 1