Edge based parameterization for tubular meshes

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. In this paper, we present an edge based parameterization method, in which the edges rather than the vertices of the mesh are treated as the target for parameterization. It improves cutting-based algorithms which cut the mesh to make it a disk topologically. The problem of cutting paths is their zigzag shape that leads to suboptimal parameterizations and finding good cutting paths is usually very difficult. Our proposed method does not need cutting of the mesh. 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. Some examples are provided to demonstrate the effectiveness of our method.