不规则多面体相交体积的逐级分解算法

将建筑工程量中沟道、基础扣减量计算等问题,归结为多面体相交交集体积的计算问题,提出了基于计算机图形学的计算不规则多面体相交体积的逐级分解算法.该算法以计算机图形学中的一些基本算法为基础,并改进了其中判断点是否在平面内的交点计数法,导出了计算公式.通过定义分割函数,使该算法无论是对凸多面体还是凹多面体的相交体积计算,都是适用的.以计算机软件实现了该算法,通过实例计算,验证了该算法的正确性.

Stepwise Decomposition Algorithm Research of the Intersecting Body Volume of Irregular Polyhedrons

We integrate the problems of deduction of intersecting grooves and bases in the constructional engineering into the problem calculating the intersecting body volume of irregular polyhedrons, and put forward the stepwise decomposition algorithm of the intersecting body volume of irregular polyhedrons based on computer graphics. The method takes advantage of the basic algorithms in the computer graphics and improves one of the algorithms which can be used to judge whether the dot is in the plane or not. By analyzing the method, we have developed the calculation formulae. Winth the segmentation function, the stepwise decomposition algorithm can be used to compute the intersecting body volume not only of the convex polyhedrons, but also the concave polyhedrons. By programming, the stepwise decomposition algorithm has been carried out, and its accuracy has been testified by a typical example.