Tubular triangular mesh parameterization and applications

Triangular meshes are a popular geometric representation for 3D models used in computer graphics. Parameterization is a process that establishes a mapping between the surface of a model and a suitable domain. This paper considers the problem of parameterizing triangular meshes that have tubular shapes. Unlike an open mesh that is of plane topological type, a tubular mesh gives rise to some special issues in parameterization due to its mesh structure. This paper presents an edge-based parameterization method, in which the edges rather than the vertices of the mesh are treated as the target for parameterization. It first parameterizes the edges on the two boundaries of the tubular mesh, then parameterizes the internal edges based on the mean value coordinates, and finally computes the parameters of the mesh vertices. The method does not need cutting of the mesh. It improves conventional cutting-based algorithms, which cut the mesh to make it a disk topologically, and overcomes the problems of cutting paths that are the zigzag paths leading to suboptimal parameterizations and the difficulty in finding good cutting paths. Some applications such as surface fitting and texture mapping are also provided. Copyright (C) 2009 John Wiley & Sons, Ltd.