平面多边形Newell公式的运用与推广

The application and promotion of the Newell formula

Newell公式在计算机图形学中常被用于计算多边形面积和平面法向量。论文主要讨论了Newell公式的运用与推广。首先将其推广三维空间中用于计算多面体体积的公式。其次讨论了在异面多边形的情况下,Newell公式的几何意义。最后,从数值计算的角度分析了Newell公式的计算方法。

The application and promotion of the Newell formula in CAGD are discussed in this paper.This formula is used to calculate the area of a plane polygon and the normal vector of the plane the polygon lies on.Firstly,it is promoted to calculate the volume of a polyhedron.Secondly,the meaning of the Newell formula is discussed if the vertices are not on the same plane.Finally,some methods are proposed to simplify the calculation of the formula.