基于曲率的三角网格孔洞修补算法的研究

在逆向工程中，三角网格模型被广泛应用。但三角网格模型常常会存在一些孔洞，这些缺陷会影响许多后续操作，因此在应用前对这些孔洞进行修补是十分必要的。一种基于曲率的空间多边形孔洞修补的算法，每次寻找孔洞多边形中夹角最小的一对邻边，构造新的初始三角片，再根据新增点和其邻点的法矢调整新增点的位置，然后更新孔洞多边形，直至覆盖整个孔洞。最后再根据需要对所有新增顶点作一定的调整。对曲率变化较小的孔洞获得较好的修补结果。

Research on the Algorithm of Hole Repairing Based on Curvature in Mesh

Triangular mesh surfaces are widely utilized in reverse engineering. However, there are some unexpected holes in the triangle mesh surfaces, and these limitations will take a negative effect on the following operations on mesh surfaces, so it is necessary to repair these holes before the following operating on the mesh surfaces. In this paper, we put forward a hole-repairing algorithm based on curvature. By searching for the adjacent edges in the hole polygon, which have the smallest angle, the new initial triangles are constructed, and the position of each new vertex is adjusted depending on the normal of itself and the normal of its adjacent vertexes, then the boundary of the hole polygon is renewed until the new generated triangles completely fill up the holes. At last, we may repeatedly adjust all the new generated vertexes on the basis of the result of hole repairing. This algorithm is adapted to repair the holes where the variation of curvature is mild and may achieve a good effect.