关键词: Newell 公式, 多面体体积, 异面多边形, 数值计算

Abstract: 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.

Key words: Newell formula, polyhedron volume, polygon with vertices not in the same
plane, numerical calculation