特征约束的四面体生成方法与案例分析

Algorithm of Mesh Generation of Feature Constraint-based Tetrahedralization

在虚拟地理环境(VGE)建模过程中,由于地学领域分析对象普遍具有边界复杂、空间特征约束较多(包括点、线、面、内洞)等特点,并且地学分析和计算对网格质量要求较高,故而难以构建能够准确顾及地学对象复杂的特征约束且满足地学分析的高质量三维网格。针对这一问题,本文提出了一种约束型Delaunay四面体网格离散算法,即首先将复杂地学对象及其各种特征约束表示为分段连续线性组合物(Piecewise Linear Complexes,PLC)中的一系列约束点、约束线段和约束面,然后利用PLC中的点集进行Delaunay四面体初始剖分,在网格离散过程中通过添加额外的节点,逐一恢复丢失的约束线段和约束面,利用限定网格单元最大半径边长比(或体积)来控制网格质量。利用该算法可以产生既满足各种特征约束条件又具有高质量的四面体网格。

In the modeling process of Virtual Geographic Environment （VGE）, as the geological objects generally have characteristics such as complex boundary, many spatial feature constraints including point, line, face and inside hole type, and meanwhile geosciences analysis and calculation require meshes with high quality, it is hard to construct three-dimensional meshes which regard for complex spatial feature constraints of geological objects exactly and have high quality for geosciences analysis and calculation. Ai- ming at this problem, a constrained Delaunay discrete algorithm of tetrahedral mesh is put forward in this paper. This algorithm first expresses constrained features of complex geological objects as a series of con- straint points, constraint segments and constraint faces in Piecewise Linear Complexes （PLC）, and then implements the initial Delaunay tetrahedral subdivision from the initial point set of the geological objects Piecewise Linear Complexes by using the Bowyer-Watson algorithm. Following the upper steps, the algo- rithm recovers the lost constraint lines and the lost constraint faces in sequence through adding some extra vertices during the mesh discrete process and it should guarantee the adding vertices do not encroach other constraint lines or constraint faces. The constraint face recovery is after the constraint line recovery and it is more difficult and complex than the constraint line recovery. In this step, some local meshes are deman- ded to reconstruct and must conform to the Delaunay empty circumsphere criterion. And then, the object model external tetrahedron elements should be deleted by adopting a marking method. After this step, it performs the mesh quality control process by restricting the maximum radius-distance ratio or the volume of tetrahedron element in the mesh. In this step, some extra vertices are also added in the tetrahedron ele- ments which can not satisfy the user restricting quality. It is proved that the algorithm can produce me- shes not only satisfying different constrained criteria but also with high quality for geosciences analysis and calculation.