POV-Ray : Newsgroups : povray.general : Minimum Distance Function : Re: Minimum Distance Function Server Time
15 Aug 2022 09:39:38 EDT (-0400)
  Re: Minimum Distance Function  
From: William F Pokorny
Date: 11 Jul 2022 06:28:24
Message: <62cbfb48$1@news.povray.org>
On 7/10/22 15:27, jceddy wrote:
> Can I inverse-transform the point being tested, run the minimum-distance
> calculation against the original data to get a minimum-distance*VECTOR*  from
> the test point to the original mesh, then just apply the object's transformation
> matrix to that vector before measuring its length?

I've never attempted a complete survey, but I'd say this the more common 
approach inside POV-Ray's code for various calculations, but it's not 
universal.

---

The numerical issues Cousin Ricky suggested as applying to the inverse 
transform in particular(a) are very complicated on the whole. Especially 
true in POV-Ray's code base where over the years numerically 
inconsistent numerical approaches were employed.

The parsing stage today flattens 'some' transforms for some shapes. 
Spheres and sphere sweeps come to mind. This kind of xfrm flattening I 
believe was done to try and help performance(b). This flattening crashes 
into the base v3.7/v3.8/v4.0 issue of pull request:

https://github.com/POV-Ray/povray/pull/358

Though, the discussion thread for that pull req goes on to look at 
additional numerical issues; including fundamental limits at the end 
related to loss of accuracy due the length of rays and polynomial 
representations for the ray-surface intersections.

We can work to reduce the exposure to numerical issues in ray tracing, 
but we can never eliminate them. More so the case due needing to use 
fast floating point hardware for good performance.

Bill P.

(a) - The span and locality of references for many 'object' 
representations are effectively better with inverse transformations 
where the working numerical space is more robust. It can be less robust 
too. However, I think this less common in practice. In other words, it 
doesn't matter if the inverse transform / result-re-transform is 
somewhat inaccurate for planet X, if all the local calculations on and 
near planet X are more accurate. I'm lying much less here where planet X 
exists in 'effective' isolation in the global numerical space of the 
scene.

(b) - The issue pull 358 is trying to address is the unfortunate 
introduction of a kind of min intersection depth filter in the "global" 
numerical space in v3.7+ which results in the trimming or elimination of 
shapes from ray-surface intersection calculations. In povr - where this 
issue fixed in a way different than the actual #358 pull req - I've got 
sphere point cloud test cases which now run 30-40% slower! Why? Well 
povr isn't ignoring 30-40% of the ray->sphere calculations. Makes me 
wonder what portion of the performance gains from the parser 
flattening/eliminating of transforms was fools-gold when measured.


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