POV-Ray : Newsgroups : povray.general : Isosurface and function pattern in v3.5 : Re: Isosurface and function pattern in v3.5 Server Time
4 Oct 2023 12:54:38 EDT (-0400)
  Re: Isosurface and function pattern in v3.5  
From: R  Suzuki
Date: 6 Sep 2001 23:42:12
Message: <3b984214@news.povray.org>
"Thorsten Froehlich" <tho### [at] trfde> wrote:
> Maybe there are any literature references on how the algorithm works?  
>Or any other detailed description? 

I have submitted a paper of the algorithm ("method 2" in the patches) 
 to an international workshop of implicit surfaces.  
But that paper was rejected. 
This would be because I do not have any background in computer 
science (my major research field is materials science).

Followings are short description of the algorithm.  It is very
simple.  If someone interested in details, I can send the rejected 
paper by e-mail.

The isosurface searching is a recursive subdivision method.  
In the first step, POV-Ray calculate the function values F(d_1) 
and F(d_2) on the ray , where d is the distance from the initial 
point and d_1<d_2.

If there is a possibility of isosurface between d_1 and d_2,
POV-Ray will calculate function value at another point 'd_3' 
on the ray between the two points 'd_1' and 'd_2'.  

The possibility is evaluated with the values F(d_1), F(d_2), 
the length from d_1 to d_2, and MAX_GRADIENT.

Then, if there is a possibility of isosurface between 'd_1' and 
'd_3', POV-Ray calculate another point between 'd_1' and 'd_3'.  
If there is no possibility between 'd_1' and 'd_3', POV-Ray 
looks for another point between 'd_3' and 'd_2', and so on.   

These calculations are carried out recursively until 

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