POV-Ray : Newsgroups : povray.binaries.images : Question regarding mesh and texture_list : Re: Question regarding mesh and texture_list Server Time
29 Nov 2022 12:02:56 EST (-0500)
  Re: Question regarding mesh and texture_list  
From: BayashiPascal
Date: 24 May 2021 03:45:00
Message: <web.60ab59244094e1f1a3e088d5e0f8c582@news.povray.org>
Thanks for your reply !


William F Pokorny <ano### [at] anonymousorg> wrote:
> 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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