>   The problem with triangulating polygons is that uv-mapping is greatly
> affected by the triangulatization process. This comes as a surprise to
> most people, but what can happen is the following:
> 
> http://www.cs.tut.fi/~warp/uvproblem.gif
> 

I don't know anything about this , but it seems quite interesting.

How would I reproduce your image in povray? Being completely ignorant, I
made this scene, hoping it would show your picture, but it does not:

#version unofficial megapov 0.7;
#declare P = pigment {
 image_map { png "uvproblem.png"
 }
}    

light_source { 0 1 }
  
mesh {   
 triangle { 0 x x+y uv_vectors 0 x x+y }     
 triangle { 0 x+y y uv_vectors 0 x+y y } 
 uv_mapping pigment { P }
 rotate x * 45
 translate <-1/2, -1/4, 1>   
}

It produces this for me: http://www.elias.f2s.com/pov/uvmap.png

-- 
#macro C(X,Y)cylinder{X*x<X,0,-Y/2>.1}#end#macro U(R,X,Y)intersection{torus{.9
.1}box{-1 0rotate y*R*90}translate<X,0,Y>scale 1-z*.5}#end union{U(0,0,0)U(1,0
,0)U(2,-1,-1)U(1,1,0)U(1,1.5,-3)U(1,2,0)U(3,1,0)U(2,2,0)U(0,3,0)U(3,2,.5)C(.1,
2)C(.8,1)C(.8,-1)C(1.1,1)C(1.9,-1)pigment{rgb 10}rotate x*90translate<-1,0,4>}

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