基于泊松标量场的任意亏格网格切割

网格切割在图形处理领域有着广泛的应用,为了更加有效和简单地得到同胚于圆盘的开网格,提出一种基于泊松标量场的三角网格切割算法.对于给定的任意网格,通过求解泊松方程构造标量场来选取临界点,并采用最速下降法给出临界点到边界或者初始点的切割路径;对于亏格不为零的网格,基于Morse理论,通过构造一个调和标量场来得到鞍点,并将它们连接到边界.该方法把任意亏格网格切割成与圆盘同胚的单边界网格,减小了在网格展开过程中产生的扭曲.实验结果表明,在给定临界点的情况下,采用文中算法得到的切割路径能很好地逼近最短路径,而且不受网格限制,适用于任意亏格的开或闭网格.

Cutting for Arbitrary Genus Mesh Based on Poisson Scalar Field

Mesh cutting is widely used in graphics.We present a more efficient and simple method based on Poisson scalar field for cutting an arbitrary genus surface mesh into a disc-like mesh.Given a mesh,we first solve a Poisson equation to construct a scalar field and use it to generate some critical points.The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method.For meshes with nonzero-genus,we construct a Harmonic scalar field,and con...