Abstract
This paper presents a shape-blending algorithm that interpolates between 2D and 3D polyhedrons. Shape blending, which is sometimes called shape metamorphosis or geometric morphing, has applications in such areas as entertainment and medical visualization. Our algorithm directly interpolates vertices of polyhedral source shapes by using variationally optimized subdivision surfaces. To interpolate a pair of 3D polyhedrons, for example, a smooth 4D tetrahedral interpolator subdivision surface is created. Intersecting the 4D subdivision surface with another 4D surface produces a blended 3D mesh. Variational optimization of the interpolator surface ensures a smooth shape transition. At the same time, manipulable nature of the interpolator subdivision surface allows for feature correspondences, shape transition effects, and other controls over the shape blending.
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