Michael Andrews <m.c### [at] readingacuk> wrote in
news:3e54d2d5$1@news.povray.org: 

...
>I surprised myself with how easy the 
> orientation macro was to write:
> 
> #macro Three_Point_Trans(T1a, T1b, T1c, T2a, T2b, T2c)
>    transform {
>      #local Y = vnormalize(T1b - T1a);
>      #local X = vnormalize(T1c - T1a);
>      #local Z = vnormalize(vcross(X, Y));
>      #local X = vcross(Z, Y);
>      #local T = Shear_Trans(X, Y, Z)
>      translate -T1a
>      transform { T inverse }
>      #local Y = vnormalize(T2b - T2a);
>      #local X = vnormalize(T2c - T2a);
>      #local Z = vnormalize(vcross(X, Y));
>      #local X = vcross(Z, Y);
>      Shear_Trans(X, Y, Z)
>      translate T2a
>    }
> #end
> 
> The three points a,b,c define a triangle; a is the origin, b-a is
> the primary orientation and abc gives a secondary orientation plane.
> The two orientation axes b-a and c-a do not have to be orthogonal,
> just independant so vcross(b-a,c-a) doesn't return a zero length
> vector. 
> 
> So Three_Point_Trans(0,y,x, P0,P1,P2) gives a transform from the
> origin to P0, aligns y with P1-P0 and puts the (x,y) plane in the
> plane of the (P0,P1,P2) triangle.
...

Here is a slightly modified version of that macro:


#macro ThreePoint_Trans(pA1, pB1, pC1, pA2, pB2, pC2)

  #local vY1 = vnormalize(pB1 - pA1);
  #local vZ1 = vnormalize(vcross(pC1 - pA1, vY1));
  #local vX1 = vcross(vZ1, vY1);
  #local T1 = transform { Matrix_Trans(vX1, vY1, vZ1, pA1) inverse }
  #local vY2 = vnormalize(pB2 - pA2);
  #local vZ2 = vnormalize(vcross(pC2 - pA2, vY2));
  #local vX2 = vcross(vZ2, vY2);
  #local T2 = transform { Matrix_Trans(vX2, vY2, vZ2, pA2) }

  transform { T1 T2 }

#end // macro ThreePoint_Trans
 

Tor Olav

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