"kurtz le pirate" <kur### [at] yahoofr> wrote in message 
news:kurtzlepirate-B3CE05.17471210112008@news.povray.org...
>
> i have 3 points in space. the plan goes through these three points can
> be defined as :
>
>  plane {vcross (P2-P1,P3-P1),0 translate P1}
>
> ok... but now, how to find angles beteewn "standard (0,x,y,z)" and this
> new "coordinate system" ?
>
> eulers's angles seem to be the solution but I do not see how to compute
> it :(
>
> any help ?

The example below shows one way, using transforms.inc to work out the 
transformation necessary.
It looks a lot of SDL, but the transform calculation is only the short bit 
in the middle, the rest is just a mass of cylinders, spheres and a plane to 
illustrate what's going on (though be prepared for the rendered image to 
look a bit messy :-) ).

The transformation is worked out in two steps. The first bit works out the 
rotation required to align the Z-axis with the new Z-axis, which I've 
assumed to be pointing from P1 to P2. The second works out the rotation 
around the Z-axis to align the Y-axis with an adjusted copy of the new 
Y-axis (derived from your calculated plane normal). After that you just need 
to assemble a complete transform (which can also include the translation to 
P1) and you've got an easy way of transposing stuff from the POV-Ray 
coordinate system to your new coordinate system.  You can also use the 
'inverse' keyword to reverse the transformation if you need to.

Regards,
Chris B.

camera {location <1,1,-4> look_at 1}
light_source { <0,100,-10>, 1 }

#include "transforms.inc"

cylinder {-10*x,10*x,0.01 pigment {rgb <1,0.5,0.5>}}
cylinder {-10*y,10*y,0.01 pigment {rgb <0.5,1,0.5>}}
cylinder {-10*z,10*z,0.01 pigment {rgb <0.5,0.5,1>}}

#declare P1 = <1,1,1>;
#declare P2 = <2,1,2>;
#declare P3 = <2,0.2,0>;
#declare NewY = vnormalize(vcross(P2-P1,P3-P1));
#declare NewZ = vnormalize(P2-P1);

// Start calculating transform
#declare ZTransform = transform {Reorient_Trans(z, NewZ)}
#declare YTransform = transform {Reorient_Trans(y, 
vinv_transform(NewY,ZTransform))}

// Construct a single transform
#declare TotalTransform = transform {
  transform {YTransform}
  transform {ZTransform}
  translate P1
}
// End calculating transform

cylinder {0,NewY,0.008 pigment {rgb <0,10,0>}}
cylinder {0,NewZ,0.008 pigment {rgb <0,0,10>}}

plane {y,0.000001
  transform {TotalTransform}
  pigment {rgbt <1,1,1,0.8>}
}

sphere {P1,0.08 pigment {rgb <1,1,1>}}
sphere {P2,0.05 pigment {rgb <1,1,0>}}
sphere {P3,0.05 pigment {rgb <0,1,1>}}

cylinder {-10*x,10*x,0.03 pigment {rgb <1,0,0>} transform {TotalTransform}}
cylinder {-10*y,10*y,0.03 pigment {rgb <0,1,0>} transform {TotalTransform}}
cylinder {-10*z,10*z,0.03 pigment {rgb <0,0,1>} transform {TotalTransform}}

box {0,0.4 pigment {rgb <1,1,0>} transform {TotalTransform}}

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