"Sybs ALHABSHI" <syb### [at] htsavoiecom> writes:

> I'm trying to find the formula and explanation about normals for smooth
> triangles. All info is helpful thanks.

The comments in the source code is the only place I know, where the
calculation of the normals is explained. It is written in triangle.c:


/*****************************************************************************
*
* FUNCTION
*
*   Smooth_Triangle_Normal
*
* INPUT
*   
* OUTPUT
*   
* RETURNS
*   
* AUTHOR
*
*   POV-Ray Team
*   
* DESCRIPTION
*
*   Calculate the Phong-interpolated vector within the triangle
*   at the given intersection point. The math for this is a bit
*   bizarre:
*
*      -         P1
*      |        /|\ \
*      |       / |Perp\
*      |      /  V  \   \
*      |     /   |    \   \
*    u |    /____|_____PI___\
*      |   /     |       \    \
*      -  P2-----|--------|----P3
*                Pbase    PIntersect
*          |-------------------|
*                         v
*
*   Triangle->Perp is a unit vector from P1 to Pbase. We calculate
*
*   u = (PI - P1) DOT Perp / ((P3 - P1) DOT Perp).
*
*  We then calculate where the line from P1 to PI intersects the line P2 to P3:
*   PIntersect = (PI - P1)/u.
*
*   We really only need one coordinate of PIntersect.  We then calculate v as:
*
*        v = PIntersect[X] / (P3[X] - P2[X])
*   or   v = PIntersect[Y] / (P3[Y] - P2[Y])
*   or   v = PIntersect[Z] / (P3[Z] - P2[Z])
*
*   depending on which calculation will give us the best answers.
*
*   Once we have u and v, we can perform the normal interpolation as:
*
*     NTemp1 = N1 + u(N2 - N1);
*     NTemp2 = N1 + u(N3 - N1);
*     Result = normalize (NTemp1 + v(NTemp2 - NTemp1))
*
*   As always, any values which are constant for the triangle are cached
*   in the triangle.
*
* CHANGES
*
*   -
*
******************************************************************************/

I hope this helps.
Thomas

P.S.: I'm curious: For what project do you need this info?

-- 
http://thomas.willhalm.de/ (includes pgp key)

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