多边形和多面体顶点法矢的数值估计

证明了两个定量，定理1揭示了三点多边的外接圆在中点处的法矢与两个边界法矢的关系；定理2揭示了四面体外接球面在中点处的法矢与三个相邻三角平面的法矢量的关系，给出了一个判别二维多维边形和三维多面体顶点法矢计算方法优劣的准则，在此基础上，提出一种用于估计三维多面体顶部的法矢量的计算方法，两个例子说明文中给出的准则和算法的合理性和实用性。

Numerical Estimation of Normal Vector at the Vertices of Polygon and Polyhedron

Two theorems are proved. One reveals the relation between the normal vector at the middle point of the circumcircle of a polygon passing through its three consecutive vertices and the normal vectors of its two edges. The other finds the relation between the normal vector at the middle point of the circumscribed sphere of a tetrahedron and the normal vectors of the three adjacent triangle planes. Two optimal criteria of the vertex normal vector estimation are presented. Based on the criterion, a new method of estimating the normal vectors at the vertices of a polyhedron is given. Examples illustrate that the new method is practical and rational.