鲁棒的多层次平面参数化

为了提高平面参数化的鲁棒性,提出一种基于多层次结构的平面参数化算法,主要包含简化和细分加点2步.对于一个拓扑同胚于圆盘的三角形网格,首先对网格进行简化并存储所简化点的拓扑信息;然后将简化后的网格映射到圆盘上;再根据所存储的拓扑信息分批次加点直至恢复出三角网格的全部顶点,并在此过程中不断地优化网格,防止三角形翻转同时使网格顶点均匀分布;最后对恢复出全部顶点的圆盘网格进行优化,得到最终的参数化网格.实验结果表明,与当前的算法相比,该算法的鲁棒性有很大的提升.

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.