Three-dimensional Geometric Metamorphosis Based on Harmonic Maps

GPlarge

Today, animations with deforming objects are frequently used in various computer graphics applications. Metamorphosis (or morphing) of three-dimensional (3D) objects is one of the techniques which realize a shape transformation between two or more existing objects. We present a new algorithm for 3D geometric metamorphosis between two objects based on harmonic mapping. Our algorithm is applicable for arbitrary polyhedra that are homeomorphic to a 3D sphere or a 2D disk. In our algorithm, each of the two 3D objects is first embedded in 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 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 interpolation.

Papers

  • Takashi Kanai, Hiromasa Suzuki, Fumihiko Kimura: “Three-dimensional Geometric Metamorphosis Based on Harmonic Maps”, The Visual Computer, Vol. 14, Issue 4, pp.166-176, 1998.
  • Takashi Kanai, Hiromasa Suzuki, Fumihiko Kimura: “3D Geometric Metamorphosis based on Harmonic Map”, Proc. 5th Pacific Graphics International Conference (Pacific Graphics ’97) (Seoul, Korea, 13-16 October 1997), pp.97-104, IEEE CS Press, Los Alamitos, CA, October 1997. [pdf (576KB)]

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