Date: Mon, 16 Dec 1996 23:40:16 GMT Server: NCSA/1.5 Content-type: text/html Last-modified: Mon, 26 Jun 1995 15:24:13 GMT Content-length: 1689 Normals

Computing the normal to a surface


There are several ways of computing a normal to a surface.
If the surface is defined as a list of triangles then one way of computing the normal is to compute the normalized cross-product of two edges of the triangle. Three vertices of a triangle are shown below as P1, P2 and P3.

If we denote

then the normal is given by


If the surface is defined as a list of general polygons then the Newell method is a good way to calculate the normal. It produces an "average" normal if the polygon is not quite planar. It also is not confused by co-linear vertices. Calculate the following, where m is the number of vertices in the polygon. The normal is then norm([nx, ny, nz]).


If the surface is defined as a parametric equation then differential methods may be used to derive the normal. If the equation for a parametric surface is

where 0<u<1 and 0<v<1 are two parameters, then the surface normal is given by


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Last modified, 6/26/95 B. Land.

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