> Date: Tue, 21 Nov 2000 17:03:45 -0600
> From: James Robertson <[EMAIL PROTECTED]>
>
> I'll obtain a normal by averaging the normals to the 6 triangles that
> surround the point.
>
> Since I'm new to 3D graphics, could anyone tell me whether this is something
> that is commonly done? Are there more sophisticated techniques (like
> weighting)? Or am I completely missing the boat?
You're doing the standard thing.
Normal averages can also be weighted according to the surface areas of the
triangles from which they're derived. You can do this easily by computing the
normals of all triangles sharing a vertex from the cross product of two edges
of each triangle, adding all the normals together, and then normalizing the
result to unit length by dividing its components by its length. This works
because the length of the vector cross product of two edges of a triangle is
half of its area.
For example, given an array of vertices, a corresponding array of vertex
normals initialized to (0, 0, 0), and triangles defined by indices into the
vertex array:
for each triangle
compute the vector cross product of two of its edges
add the vector cross product to the accumulated normals at each its vertices
for each vertex
normalize the corresponding normal vector sum to unit length
Be sure to to multiply the edges in the order corresponding to the order of the
vertices to avoid cross products pointing in the wrong direction; e.g., given a
triangle defined by points a, b, c in that order, compute the cross product as
(b-a)X(c-b) or (c-b)X(a-c) or (a-c)X(b-a) or (b-a)X(c-a) or (c-b)X(a-b) or
(a-c)X(b-c).
There are also techniques which look at threshold angles between triangles to
determine if the angle is too steep to average the normals, which allows "hard"
edges between triangles at the expense of creating more vertices.
The GeometryInfo utility class can do all this for you.
-- Mark Hood
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