Ooops.
I think that my "Intersection at one or two edges"
comment in the code I just posted is wrong.

See my new RayIntersectsTriangle() macro below.

If one does not want the edges and vertices to count as
part of the triangle, then just replace the >= and <=
operators below with > and < operators.


Tor Olav


Tor Olav Kristensen wrote:
>...
> I think that my RayIntersectsTriangle() macro in the code below
> provides such a shortcut (*), but I'm not sure yet if it is optimal.
>...
> // ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
> // Copyright 2002 by Tor Olav Kristensen
> // Email: tor### [at] hotmailcom
> // http://www.crosswinds.net/~tok/povray
> // ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
> 
> #version 3.5;
> #include "colors.inc"
> 
> // ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
> // Intersection macros
> 
> #macro RayIntersectsTriangle(pRay, vRay, pA, pB, pC)
> 
>   #local vRA = pA - pRay;
>   #local vRB = pB - pRay;
>   #local vRC = pC - pRay;
>   #local vABN = vcross(vRA, vRB);
>   #local vBCN = vcross(vRB, vRC);
>   #local vCAN = vcross(vRC, vRA);
>   #local STP = vdot(vABN, vRC);
>   #if (STP = 0)
>     #debug "Macro RayIntersectsTriangle: "
>     #debug "Degenerate triangle or "
>     #debug "origin of ray lies in same plane as triangle\n"
>     #local Intersect = false;
>   #else
>     #local AB = vdot(vRay, vABN);
>     #local BC = vdot(vRay, vBCN);
>     #local CA = vdot(vRay, vCAN);
>     #if (AB = 0 | BC = 0 | CA = 0)
>       #local Intersect = true; // Intersection at one or two edges
>     #else
>       #if (STP > 0)
>         #local Intersect = (AB > 0 & BC > 0 & CA > 0);
>       #else
>         #local Intersect = (AB < 0 & BC < 0 & CA < 0);
>       #end // if
>     #end // if
>   #end // if
> 
>   Intersect
> 
> #end // macro RayIntersectsTriangle

#macro RayIntersectsTriangle(pRay, vRay, pA, pB, pC)

  #local vRA = pA - pRay;
  #local vRB = pB - pRay;
  #local vRC = pC - pRay;
  #local vABN = vcross(vRA, vRB);
  #local vBCN = vcross(vRB, vRC);
  #local vCAN = vcross(vRC, vRA);
  #local STP = vdot(vABN, vRC);
  #if (STP = 0)
    #debug "Macro RayIntersectsTriangle: "
    #debug "Degenerate triangle or "
    #debug "origin of ray lies in same plane as triangle\n"
    #local Intersect = false;
  #else
    #local AB = vdot(vRay, vABN);
    #local BC = vdot(vRay, vBCN);
    #local CA = vdot(vRay, vCAN);
    #if (STP > 0)
      #local Intersect = (AB >= 0 & BC >= 0 & CA >= 0);
    #else
      #local Intersect = (AB <= 0 & BC <= 0 & CA <= 0);
    #end // if
  #end // if

  Intersect
      
#end // macro RayIntersectsTriangle

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