关于离散参数曲线网上曲率的一种刻画

针对由参数曲线网形成的四边形网格,提出了一种简洁快速的加细方法,即在保持初始网格不变的情况下,使每一个小极限曲面片为C2,而整体极限曲面为一次连续的.应用该方法,给出了一种四边形网格上任意顶点处的离散估计值的定义方法,主要包括离散的Gauss曲率和平均曲率的定义.最后,实验验证表明了该方法的有效性和优越性.

A kind of definition of curvatures on discrete parametric curves net

To get a more efficient numerical method of computing the discrete curvatures of a surface, a new subdivision rule of the discrete parametric curves net is proposed, that is, in the case of keeping initial network, each of limit surface is C^2, and the unitary limit surface is C^1. Applying this rule, a kind of the definition of the discrete estimated value on the quadrilateral net is given. It includes the definition of discrete Gauss curvature and discrete mean curvature. At last, the validity and superiority of this definition are illustrated by numerical experiments.