

"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 POVRay 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.dimensionsmath.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 POVRay.
That looks like an nice and interesting film. Thank you.

Tor Olav
http://subcube.com
https://github.com/tok
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