POV-Ray : Newsgroups : povray.binaries.images : Isosurface from magnitude of complex function with domain coloring : Re: Isosurface from magnitude of complex function with domain coloring Server Time
28 Jan 2022 22:57:21 EST (-0500)
  Re: Isosurface from magnitude of complex function with domain coloring  
From: Tor Olav Kristensen
Date: 28 Dec 2021 19:25:00
Message: <web.61cbaa036041c67040964eff89db30a9@news.povray.org>
"Bald Eagle" <cre### [at] netscapenet> wrote:
> Knowing partly what goes into all of this, I can see that it required a lot of
> time and attention to detail - and you always post fairly polished images, even
> if they are only WIPS.

Yes, it takes some time, but as long as it's interesting work I don't mind.

I seldom have time to polish finishes, textures or materials, so I mostly use
the default ones. But I do spend some time on the pigments and where to place
the light source and the camera.

> > I'm not very familier wit Paul Nylander's work. Those macros seem like a good
> > start for a library for complex calculations. But the Pow() macro could need
> > some work to allow for the exponent to also be a complex number.
> http://bugman123.com/index.html

Yes, I have seen his web pages some years ago, but I have never looked very
closely at them. They are quite "busy" with a layout that makes them a bit hard
to read - but they have many interesting topics. AFAIK he too lives in Norway.

> Complex exponents --- Oh, it makes my head hurt to even thing about that.


    A^B = e^ln(A^B) = e^(B*ln(A))

    pow(A, B) = exp(B*ln(A))

You already have formulas for complex exp() and multiplication - and
implementing ln() is not very hard.

> > I'm also wondering how hard it would be to use mod()
> > to have an infinite array of those "black hole vortices" on a plane - in either
> > a rectangular or an alternating/hexagonal arrangement...
> That's an interesting idea: to have a mod() operator that can handle complex
> values. But I don't know how to implement that...

Yes, that could be a way to create such repetitive patterns.

But it would be even better if a POV-Ray library could be made that can preserve
the repetitive nature of several of the complex operators (i.e. those that are
multi valued). I think that that would be quite hard to make...

> Maybe check out
> http://www.dimensions-math.org/Dim_E.htm
> and perhaps get in touch with the authors, since they seem to have an amazing
> grasp of both the math as well as POV-Ray.

That looks like an nice and interesting film. Thank you.

Tor Olav

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