2D and 3D Shape Morphing (Metamorphosis)
by Using Subdivision Surfaces

Ryutarou Ohbuchi
Yamanashi University, Yamanashi, Japan.
Shigeo Takahashi
Gunma University, Gunma, Japan.
Yoshiyuki Kokojima
Gunma University, Gunma, Japan.

We have been working on a new geometric morphing algorithm for polygons and polyhedrons. The algorithm is capable of morphing between shapes having different genera, e.g., between a sphere and a torus, with little intervention. At the same time, the algorithm offers powerful control over the morphing process; for example, user-specified evolution of topology, vertex-to-vertex feature correspondence, representation of both smooth and sharp features, user-specified deformation of shapes during the morph, and spatially non-uniform progress of the morphing.
Our algorithm directly interpolates vertices of polyhedral source shapes by using subdivision surfaces. The algorithm employs variational optimization to produce (N+1)-dimensional subdivision surfaces by treating vertices of the N-dimensional polyhedrons as geometric constraints. For example, three-dimensional (3D) polyhedrons are interpolated by four-dimensional (4D) subdivision (hyper-)surfaces. Morphed shape can be extracted by intersecting the subdivision surfaces with another (N+1)-dimensional surface. Smoothness of subdivision surface gives us smooth shape transitions while manipulability of the subdivision surfaces gives us powerful control over the morphing, which include feature correspondence and shape transition control

Topological transition control

Spatial transition control

3D morphing