基于曲面方程的三角形网格模型求交方法

A Method for Obtaining the Intersections in Triangular Mesh Model Based on the Surface Equation

在应用GIS不规则三角网的地层建模、表达和分析的研究过程中,会涉及到大量复杂的三角网格模型的求交运算。本文提出了一种基于曲面方程的三角形网格模型求交算法。该算法首先通过三维点要素,插值拟合出两个曲线方程,然后求解方程组获得交线方程,再将该交线分别投影到三角形网格上,获得顺序的投影三角形组,最后对两个三角形组做求交运算。该算法能快速有效地排除不相交三角形,同时,对候选三角形和三角形交线依次记录,大大减少了运算时间。

With the GIS formation modeling based Triangulated Irregular Network,expression and analysis,it is involved a lot of complicated calculations in the triangular mesh intersection model. This paper was presented a method of calculation in triangular mesh intersection model which based on the surface equation. First,two curve- surfaces equation can be fitted to the Interpolation of three-dimensional point features,and the intersection equation are obtained by solving these equations. Secondly,by projecting the intersections to the two triangle meshes,ordinal groups of projected triangle can be obtained. Finally,the intersections calculation of the two groups of triangle. The disjoint triangles can be rapidly excluded in the algorithm,and the candidate triangles will be recorded at the same time,so it greatly reduces the computing time.