一类复杂区域的网格优化算法

摘要

In recent years,freeform design has been widely used,especially in the field of architectural freeform design.There are many kinds of methods to approximate a freeform shape.One method is to approximate a freeform shape with a planar quadrilateral (PQ) mesh.So the quality of the PQ mesh directly affects the quality of the freeform shape design.This paper describes a planar quadrilateral mesh optimization algorithm.We first determine the complex regions,and combine up-sampling and fairing algorithms,then totally combine planar quad mesh with subdivision method.By this method,the freeform shapes not only improve the quality,but also have the aesthetic.%近年来自由曲面设计得到了广泛应用,尤其在建筑曲面设计领域.逼近自由曲面的方法有很多种,一种方法是采用平面四边形网格(PQ网格)逼近自由曲面,所以平面四边形网格的质量直接影响了自由曲面设计的质量.介绍了一种平面四边形网格优化算法,判断出复杂区域,采用局部采样点加密和光顺方法相结合进行处理,在整体上采用平面化和细分方法相结合策略优化网格.通过该方法,生成的自由曲面不仅质量得到了提高而且具有了美学效果.