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．