POV-Ray : Newsgroups : povray.advanced-users : Mathematical "Primitive" vs Isosurface : Re: Mathematical "Primitive" vs Isosurface Server Time17 Sep 2021 05:31:05 EDT (-0400)
 Re: Mathematical "Primitive" vs Isosurface
 From: Warren Date: 13 Oct 2019 06:00:01 Message:
```
{
"@context": "https://schema.org",
"@type": "DiscussionForumPosting",
"@id": "#web.5da2f4b465080b019e68eb1f0%40news.povray.org",
"headline": "Re: Mathematical \"Primitive\" vs Isosurface",
"dateCreated": "2019-10-13T10:00:01+00:00",
"datePublished": "2019-10-13T10:00:01+00:00",
"author": {
"@type": "Person",
"name": "Warren"
}
}
Hello/Hi,

I remember in school my mathematics teacher told me that for the equation of 6th
degrees and above it was impossible to find roots with a perfect method (that
characteristic has been demonstrated). The functions in isosurface primitive can
use any degree equation (the parametric function which indicates that for any
(x,y,z) set, we are on volume surface if it is equal to zero, if the result is
negative we are inside or outside if positive. So in povray, the point is to
find roots (zero equality) for intersections. This said, how can POVRay find
roots of 6th and above degree equations ?

The isosurface uses the Newton's approximation to find roots of the isosurface:
https://en.wikipedia.org/wiki/Newton%27s_method

This last method while not perfect (some equations tend to give almost infinite
results the closer you are from a x value and since Newton's method is an
approximation this can take a very long time to find the root), so to not spend
a very long time testing value for intersections the 'accuracy' parameter of
isosurface can be set to something like 0.0001 for example to abort further
approximation of a single root if Newton's method find a result of 0.0001 or
less (not perfectly 0 I mean).

My english is not perfect, I apologize for any writing error. :-D
```