Mesh parameterization with a virtual boundary

Parameterization of a 3D triangular mesh is a fundamental problem in various applications of meshes. The convex combination approach is widely used for parameterization because of its good properties, such as fast computation and one-to-one embedding. However, the approach has a drawback: most boundary triangles have high distortion in the embedding compared with interior ones. In this paper, we present an extension of the convex combination approach that resolves the drawback by using a virtual boundary. Since the virtual boundary is fixed onto a given convex polygon instead of the real boundary, the real boundary triangles can better reflect the shape of the corresponding 3D triangles. The proposed approach obtains a parameterization of a 3D mesh with less distortion than with the original convex combination approach. r 2002 Elsevier Science Ltd. All rights reserved.