William F Pokorny <ano### [at] anonymousorg> wrote:

> None can be that important given how long they've not been done! :-)

Well, yes.   There's that.
But one might equally ascribe their non-usage to their non-existence.

Given an easy way to do something, people usually take it.
If faced with the prospect of somehow getting someone somewhere to write a
mapping in source code and provide a new release - or - just writing some "good
enough" pseudo-mapping or function-mapping, then maybe that's what's been done.
No idea how many people (would have) use(d) those other types of maps, but
possibly that would tip the scales the other way.

It's always hard to speculate about these things accurately.  ;)

> Guessing a  at meaning/application, the parabolic I suppose might
> occasionally be of use - parabolas.

I guess maybe there might be further use with parabolic mirrors, cameras, and -
more specifically - telescopes.

https://www.eso.org/sci/facilities/paranal/telescopes/vlti/tuto/tutorial_introduction_to_stellar_interf.pdf

> Taking the hyperbolic to mean
> non-linear in some aspect of other usually linear mappings, that I guess
> that would end up as a set of 'hyper' mappings for linear, spherical,
> etc.

I looked - it seems like they might be very useful and fun for Escher fans.
M. Grimbert might be interested, given he seems to be the master of tilings.
I'm guessing/speculating that these mappings (Poincare disks, etc) might have
practical engineering / scientific use in physics, Finite Element Methods, fluid
dynamics, etc?

https://computergraphics.stackexchange.com/questions/2117/map-a-texture-onto-a-hyperbolic-triangle
https://medium.com/@philogb/hyperbolic-floors-a2c5445144c6
https://mediatum.ub.tum.de/doc/1210572/1210572.pdf

Or maybe it has specific application to cartography and map projections?
https://en.wikipedia.org/wiki/Squeeze_mapping

It might also be related to a catadioptric omnidirectional camera mapping, like
that used with a hyperbolic convex mirror.
https://link.springer.com/content/pdf/10.1007%2F978-3-642-02921-9_26.pdf

And this leads me to believe that they are all related:
http://roguetemple.com/z/hyper/models.php



> Piriform suppose might have been aimed at two element blobs or
> something?

Possibly.   No idea why it was desired in v 1 of all things, and the only places
I find it aside from pure math sites, is references for POV-Ray (with Mike
Williams bridging that gap)
https://mathworld.wolfram.com/PiriformCurve.html
https://mathworld.wolfram.com/PiriformSurface.html

>
> My up front issue with all more complicated mappings - and with the more
> complicated shape uv_mapping options - is one should first and foremost
> work out how the maps can easily be created in POV-Ray(1). Or, know of
> some standard external 'standard' like the light probe angular mapping
> added to v3.8. Otherwise, you've got some feature you can 'advertise'
> and which might look great for a demo or two, but in the end it's a
> feature pretty much nobody uses.
>
> (1) - Matching cameras, an interactive painting capability, ...
>
> Aside: Most any complicated mapping can be accomplished today via
> functions - though it might not be easy to get right, as you well know.

Of course.   But sometimes these things inexplicably take on a life of their
own.  And during the course of investigating them simply out of curiosity,
novelty, or someone's specialized interest or based solely on the challenge of
doing it - we uncover bugs (!) and discover interesting new things that we might
never have thought of or even known were possible.

Just figured I'd ask - because obviously _someone_ thought they were important
enough to assign a mapping slot for them early on.

##############################################################################

Now, given the fact that we have uv-mapping for Bezier bicubic patches, and the
source code to create the patch from the corners and control points:

Do we think it would be a lot of work to add a feature where
colors/pigments/textures/finishes could be specified at the corners of a Bezier
patch, and a pattern / map would be generated based on the patch?
https://www.ibiblio.org/e-notes/Splines/color3d.html
(I didn't SEE such a thing in HGpovray38, but I might have missed it)

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