应用高斯曲率积分的曲面可展化分片方法研究

Developable surface partition algorithm based on Gaussian curvature integration

对空间曲面的分片算法进行了研究,以高斯曲率的绝对值对面积的积分与曲面面积的比值作为曲面分片系数,并以各曲面单元分片系数的和作为曲面分片的控制值。在给定分片控制值的约束条件下,通过对任意空间曲面进行离散化、反算拟合及曲面单元累加实现曲面分片。控制各曲面片分片系数累加值使之小于一定的控制值以使各分片近似可展。以空间双曲曲面为算例对分片算法的有效性进行了验证。

A surface partition algorithm is presented in this paper.The partition coefficient for a surface partition is defined as the ratio of the integration of the absolute value of Gaussian curvature of the surface to its area.The controlling value for the surface partition is defined by the summation of the partition coefficient of the accumulated surface elements.A doubly curved surface is divided into several patches through discretizing, re-fitting and surface element accumulating with the controlling value of surface partition is given.The partitioned surface patch can be approximately developed by controlling the summating value of the accumulated surface elements within certain controlling value.An example is given to show the effectiveness of the algorithm.