| Abstract: | The issues relating to the shape transformation problem are discussed and a new algorithm is presented for computing the transformation of one shape into another. In this algorithm, the boundary definitions of the two initial shapes are used and a mapping is established between the vertices and edges of the respective objects. New vertices and edges are introduced into the object definitions when necessary to establish a one-to-one vertex correspondence and to match connectivity relationships between vertices. These can then be used to do a vertex-to-vertex interpolation that maintains valid polyhedral topologies for all of the intermediate shapes. The algorithm establishes a mapping between areas of the object such that adjacency relationships are preserved. These areas are recursively subdivided so that adjacency relationships of subareas are also preserved. During subdivision, vertices and edges are added to the boundaries of subareas so that a one-to-one mapping is established between them. Subdivision continues until each subarea consists of a single face. The algorithm presented works for objects that are topologically equivalent to spheres and can easily be extended to other pairs of objects as long as they are topologically equivalent to each other. |
