Polyhedron realization for shape transformation

Polyhedron realization is the transformation of a polyhedron into a convex polyhedron with an isomorphic vertex neighborhood graph. We present in this paper a novel algorithm for polyhedron realization, which is general, practical, efficient, and works for any zero–genus polyhedron. We show how the algorithm can be used for finding a correspondence for shape transformation. After the two given polyhedra are being realized, it is easy to merge their vertex–neighborhood graphs into a common graph. This graph is then induced back onto the original polyhedra. The common vertex–neighborhood graph allows the interpolation of the corresponding vertices.

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