Robust Hierarchical Planar Parameterizations

In order to improve the robustness of planar parameterizations, we propose a novel hierarchical algorithm. The algorithm contains two procedures: decimation and subdivision. For a triangle mesh which is homeomorphic to disk, we decimate it firstly and store the topological information of the decimated vertices.Secondly, we map the decimated mesh into disk, subdivide the mesh and insert vertices flexibly according to the information stored until all of the vertices are restored. We optimize the mesh during the period to avoid flipping and make vertices distribute evenly meanwhile. Finally, we optimize the mesh and acquire the parameterized result. Compared with state-of-the-art methods, the experiments show that our algorithm performs better in robustness.