基于Laplacian算子的法向网格生成

多分辨率法向网格是网格的一种多分辨率表示方法。其中每一个分辨率层次都是它的前一层法向的偏移，因而除基网格顶点外，其它顶点都可表示为一个标量形式。本文提出一个生成法向网格的算法，对Lgor Guskov等人的方法作了改进，首先，在计算基网格的网格简化过程中，记录下每个基网格三角形在原始网格中的相关三角形集，以此来提高求交效率同时仍保证较高的准确性。其次，增加了处理边界情形的能力。最后，利用Lapacian算子的切向分量对法向网格进行重新参数化。使得网格的三角形分布更均匀，三角形的形状也更为正则。从实验结果可以看到，本文的算法具有较强的实用性，所得到的法向网格与原始网格的逼近误差也很小。

Normal Mesh Generation Based on Laplacian Operator

A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version Hence each vertex of the mesh can be stored as a scalar value except for the vertices of a base mesh An algorithm for generating the normal mesh is presented by improving the method of Guskov et al An associated triangle set for each triangle of the base mesh in the process of mesh simplification is recorded firstly for enhancing efficiency and sustaining exactness, then the models with boundaries is treated in similar way Moreover, the Laplacian operator is employed to optimize the distribution and the shape of triangles of the normal mesh Through the experiment, it is found that the present method is feasible and the error between the original mesh and the approximate mesh is very small