任意实体网格模型体积的适应性计算

Evaluating Volumes of 3-D Models Based on Adaptive Division

在分析三维模型数据表示结构的基础上,提出一种计算三维实体模型体积的适应性方法。首先用一组等距的平行平面对网格模型进行分层剖分,并利用平面简单多边形的带符号面积公式求取相应截面的面积,然后根据相邻平面间的距离估算模型体积。该方法可根据给定的误差阈限适应性地快速计算模型体积的逼近值,或以一定的时间代价求模型体积的精确值以及模型体积的分布特征。实验表明,相应的计算程序运行稳定、快速,可以处理具有任意几何和拓扑复杂性的实体模型。

Based on analysis of data structure for representation of 3 -D mesh models, we propose a method to calculate value of volume of arbitrary 3 -D solid model by employing an adaptive division strategy. The method first divides a model into several segments by using a set of parallel planes, and then calculates the signed areas of cross sections on the planes according to the area formula of planar simple polygons. Volume values, which are between each two adjacent sections, of the solid model can consequently be calculated in virtue of the areas and distances between the adjacent sections. By collecting the values, the total volume of the model can be obtained. Our method not only can calculate volume of 3 -D model approximately and adaptively according to a threshold given by user, but also can give accurate value of model volume when some time cost is spent or extract the volume distribution of models. Experiments show that our method can run robustly and quickly even on personal computer, and can process models with arbitrary geometry and topology.