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

> I ran across the following in the v1.0 source code the other day while
> trying to understand the history of something:
>
> /* Image/Bump Map projection methods */
> #define PLANAR_MAP      0
> #define SPHERICAL_MAP   1
> #define CYLINDRICAL_MAP 2
> #define PARABOLIC_MAP   3
> #define HYPERBOLIC_MAP  4
> #define TORUS_MAP       5
> #define PIRIFORM_MAP    6
> #define OLD_MAP         7

VERY cool  :)
It's more than clipka uncovered.
So at least that answers a 6-year-old question.  :D

http://news.povray.org/povray.binaries.images/message/%3C5438051b%241%40news.povray.org%3E/#%3C5438051b%241%40news.povr
ay.org%3E

Are these mapping types still in need of development?

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On 8/24/20 1:35 PM, Bald Eagle wrote:
> William F Pokorny <ano### [at] anonymousorg> wrote:
> 
...
> 
> Are these mapping types still in need of development?
> 

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

Guessing a  at meaning/application, the parabolic I suppose might 
occasionally be of use - parabolas. 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. Piriform suppose might have been aimed at two element blobs or 
something?

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.

Bill P.

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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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> 
>
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


An investigation not as pattern but as warp could be interesting.

The early part to answer is: what happen outside the circle.
One answer can be: nothing, outside the circle, there is no transformation.

Or something different, as suggested in the pdf for poincarré disk.

It is "of course" to be mainly used with the image pattern, so it is
better from the very start that the reference plane be the same (to
avoid a systematic rotate), and the third coordinates is to be dropped.

So far the "perfect" illustration could be some pedestal table with such
topping, and some chess set on it...
With an outer ring, which implies some layered textures too.

*********

About bezier bicubic patches, I do not so far understand what is the
final purpose of the request. Does it sound like gluing the mesh camera
to a bezier bicubic patch ? (mesh camera or user-function defined camera).
As a raytracing aims at generating pictures, what is a finish map in
that context ?

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Le_Forgeron <jgr### [at] freefr> wrote:

> An investigation not as pattern but as warp could be interesting.

Aha, yes - that's a better way of thinking about it.

> The early part to answer is: what happen outside the circle.
> One answer can be: nothing, outside the circle, there is no transformation.

That would be my initial, naive impression.  Something like "once".

> Or something different, as suggested in the pdf for poincarré disk.

I'm sure that there exist a number of different options, and of course we will
probably find out what they are once someone picks up this sort of thing to
begin experimenting with and proceeds to discover what other ways there are or
follows a path of reasoning to suggest a new option.

Geometric inversion?

> It is "of course" to be mainly used with the image pattern, so it is
> better from the very start that the reference plane be the same (to
> avoid a systematic rotate), and the third coordinates is to be dropped.

Oh, please, no.   One of my main dislikes of things like prism {} is that the
coordinates are supplied in <x, z> format.  So then rather than simply passing
[multipurpose] vectors to the object definition, where the y-component gets
_ignored_, I have to write a whole new section of code to convert everything
into a special single-purpose format.   :(

> So far the "perfect" illustration could be some pedestal table with such
> topping, and some chess set on it...
> With an outer ring, which implies some layered textures too.

Likely.  But I also envisioned seeing how all of the various tilings can be
manipulated.   :)

> About bezier bicubic patches, I do not so far understand what is the
> final purpose of the request. Does it sound like gluing the mesh camera
> to a bezier bicubic patch ? (mesh camera or user-function defined camera).
> As a raytracing aims at generating pictures, what is a finish map in
> that context ?

The idea would be to define 4 corners of the bezier patch in terms of - not
<x,y,z> - but <r, g, b> and then rather than doing a straight bilinear
interpolation of the color values between the two points across the rectangle,
bicubically interpolate the colors across a Bezier surface.
Does that make sense?

I guess I also had it in my mind that if I had an existing _geometric_ bezier
patch, that somehow it would be possible to simply define the colors of the 4
fixed corners, and those would get mapped to the geometric coordinates.   Then
the geometric control points would control the bicubic color interpolation
between the color values - avoiding the need to write a whole separate block of
code for the coloring.

I hadn't really though it all the way through, so sorry for any confusion.

But it does suggest that there could be a bicubic WARP where patterns could be
distorted (or image maps corrected) through such a mechanism.

Also, the mesh camera is an interesting idea.  I'm not sure what you mean by the
finish map - but I would imagine it has something to do with the
ray-scene/surface angles?   Like for something simple like specular reflection?
That I simply don't know.
Maybe if it were just an experimental feature, use the undistorted mesh camera
to generate the color but the bicubic functions to control the view....
No idea.

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