基于逐点插入法的定尺度三角剖分算法研究

Research on Scaling Triangulation Algorithm Based on Point by Point Insertion Method

在三角网剖分过程中,三角形是否均匀是决定三角网是否高质量的重要因素,在构网中形状不规则的三角形被称为病态三角形。为了减少构网中病态三角形的数量,本研究在传统逐点插入法的基础上,对凸包边界进行细化,生成边界精度较高的新凸包。运用定尺度剖分法对整体三角网进行筛选,对筛选出不符合尺度的三角形进行合并,生成较为均匀的三角网。试验表明,与未设定剖分尺度的图形相比,经过设定尺度后生成的三角网更均匀,所以通过设置剖分尺度能够有效地减少构网中的病态三角形数量。

In the triangulation process,whether the triangles are uniform or not is an important factor to determine whether the triangulation is of high quality.In the network construction,the irregular triangles are called ill conditioned triangles.In order to reduce the ill conditioned triangles in the network construction,this research refines the convex hull boundary based on the traditional point by point insertion method,and generates a new convex hull with high boundary accuracy.The overall triangulation is screened by using fixed-scale triangulation,and the triangles that do not meet the scale are obtained,which are combined in the next step to generate a more uniform triangulation.The experiment shows that the triangulation network generated after setting the scale is more uniform than the graphics without setting the division scale.Therefore,by setting the partition scale,the number of ill conditioned triangle in network construction is effectively reduced.