Shay wrote:
> 
> This question didn't make much sense the first time I wrote it. Let me try
> again.
> 
> How can I calculate the normal of a vertex which lies on the side of a
> triangle. but not at the corner?
>  ___________
>  |\       /|
>  | \  B  / |
>  |  \   /  |
>  |   \ /   |
>  | C  X    |
>  |   /     |
>  |  /   A  |
>  | /       |
>  |/________|
> 
>  How would I calculate the normal at point X given the normals of triangles
> A, B, & C?


Shay, there are several possible ways to calculate
such a normal. It all depends on the application.

But assuming that you are going to use it in
a mesh2{}, then I would recommend the following:

If vN_A, vN_B and vN_C are normals with unknown
length, then I would suggest this for the normal
vector at X:

#declare vNormalX =
vnormalize(
  vnormalize(vN_A)*AreaA
 +vnormalize(vN_B)*AreaB
 +vnormalize(vN_C)*AreaC
)


If you know the coordinates of the corners p00,
p10, p11 and p01, then I would suggest the
following:

 p01_______p11
  |\       /|
  | \     / |
  |  \   /  |
  |   \ /   |
  |   pXX   |
  |   /     |
  |  /      |
  | /       |
 p00_______p10

#declare vNormalX =
vnormalize(vcross(p01 - p10, p11 - p00))


I would also recommend the same formula even
if the triangles were arranged like this:

 p01_______p11
  |\       /|
  | \     / |
  |  \   /  |
  |   \ /   |
  |   pXX   |
  |   / \   |
  |  /   \  |
  | /     \ |
 p00_______p10



The argument for this involves some vector
cross product calculations (which I can try to
show and explain if you're interested).

Note that I have not tested my suggestions
above yet, so there may be defects in my
reasoning.


Tor Olav

Post a reply to this message