Date: Mon, 16 Dec 1996 23:40:16 GMT
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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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