三维约束Delaunay三角化的边界恢复和薄元消除方法

提出一种有效的三维约束Delaunay三角剖分的边界恢复算法，该算法综合了P．L．George算法和N．P．Weatherill算法的优点，通过将约束边和约束面加以恢复，保持了实体边界的完整性，解决了经典Delaunay算法不能剖分凹域的问题，从而实现了复杂三维实体的网格剖分。提出了一种简易而有效的消除薄元方法——薄元分解法，彻底解决了三维Delaunay三角剖分过程中所产生的薄元问题。实践证明，本文提出的边界恢复算法和薄元消除算法健壮有效，生成网格的质量高，并且易于实现。

Boundary restore algorithm and sliver elimination of 3D constrained delaunay triangulation

An effective algorithm is proposed in this paper to restore the solid boundary for 3D constrained Delaunay triangulation in finite element mesh generation. The algorithm combines the advantages of methods given by P.L. George and N.P. Weatherill. By restoring constraint segments and triangular facet seperatively, the integrity of solid boundary after mesh could be maintained. So the constrained Delaunay triangulation method can be applied to generate mesh on any complex convex and concave 3D solids. In order to tackle the sliver element problem commonly existing in 3D Delaunay triangulation, a method called sliver decomposition is proposed. By decomposing sliver elements and their adjacent tetrahedral elements, all sliver elements under specified quality factor can be removed. The two algorithms are proved to be robust, efficient and easy to be implemented in practical appplications.