On 5/24/21 12:25 AM, BayashiPascal wrote:
> Hi everyone,
> I have a question regarding texture_list applied to mesh of very small size.
> I've noticed that in such case artifacts appear in the texture. I can avoid the
> problem by scaling up the input mesh (generated by another app), and scaling it
> back down in the POV-Ray script, but if possible I'd like to avoid that.
> I guess this is a problem related to numerical accuracy, so maybe there is a
> parameter somewhere that would help ?? Or, is there something else I'm not aware
> of, and doing wrong ?

Yes, numerical accuracy it is.

In the POV-Ray source there is a defined EPSILON value of 1e-10 which 
over time tended to be used whenever someone had need of a small 
'epsilon' value.

However, there isn't a one size fits all EPSILON value. It depends on 
the math being done. In triangle.cpp there is a function:

SmoothTriangle::Calculate_Smooth_T(..._)

with some code which reads:

     if(dm1*dm1<EPSILON)
     {
         if(dm2*dm2<EPSILON)
         {
             if(dm3*dm3 < EPSILON)
             {...

Using an 'epsilon' value of gkDBL_epsilon (~4.4e-16) which is generally 
good for simpler double math, the textures for both your triangles 
interpolate well.

The updated code looks like:

     if(dm1*dm1 < gkDBL_epsilon)
     {
         if(dm2*dm2 < gkDBL_epsilon)
         {
             if(dm3*dm3 < gkDBL_epsilon)
             {...

Note. There's still a numerical limit to hit if you make things small 
enough. In fact, in the very corners of each triangle it's probably 
still tripped sometimes for the conditionals above; We just can't see it.

Bill P.

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