"MichaelJF" <mi-### [at] t-onlinede> wrote:
> No, no non-Euclidian math is needed here. One can solve the puzzle only with
> Euclid and Pythagoras but one has to think in polar coordinates instead of
> Euclidian ones and heavily use rotate.

Isn't that non-Euclidian?

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Nice

"MichaelJF" <mi-### [at] t-onlinede> wrote in message 
news:web.51f026863a6d0c047d40b13d0@news.povray.org...
> "MichaelJF" <mi-### [at] t-onlinede> wrote:
>> clipka <ano### [at] anonymousorg> wrote:
>> > Am 24.07.2013 16:19, schrieb Cousin Ricky:
>> > > "Shay" <non### [at] nonecom> wrote:
>> > >> If you think you've got it figured out, try it. $50 to the POV-Ray 
>> > >> wishlist
>> > >> (presuming this still exists) if anyone else can get it.
>> > >
>> > > I can visualize the parts that need to fit together.  The hard part 
>> > > will be the
>> > > non-Euclidian math needed to make them match up.
>> >
>> > Indeed!
>>
>> No, no non-Euclidian math is needed here. One can solve the puzzle only 
>> with
>> Euclid and Pythagoras but one has to think in polar coordinates instead 
>> of
>> Euclidian ones and heavily use rotate. I really liked this Little 
>> challenge
>> since I was a Little bit bored looking at Smoking mountains and needed a 
>> break.
>> But unfortunatelly I have not the time to accomplish the full Picture.
>>
>> Best regards,
>> Michael
>
> To illustrate this a bit. If you add a new slice of the surrounding sphere 
> and
> cut out the blue "circles" rotated eight times around the y-axis, fill in
> appropriate scaled, cut and transformed tori and finally eight little 
> spheres
> you have solved the problem of the upper pikes.
>
> Best regards,
> Michael
>

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"Shay" <non### [at] nonecom> wrote:
> No blobs, SORs, isos, etc. Just the primitive primitives.
>
> Maybe I'm off my game, but this one took some head-scratching. 559 pieces
> with the bounding and clipping objects.
>
> If you think you've got it figured out, try it. $50 to the POV-Ray wishlist
> (presuming this still exists) if anyone else can get it.
>

I thought I was pretty good at CSG but this is amazing, I can see how I would
try it but my method relies more on basic math and trial and error rather than
anything scientific ;-)

The bevelling is the bit I would have most trouble with, unfortunately not a
good time for me to be attempting this but maybe in a few weeks I will find some
time to have a go, I like a challenge.

Sean

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I can't say exactly how close MichaelJF is, but I can say with confidence
that he may very well be further away that it seems. What made a monkey out
of me wasn't the difficulty (though, Euclidian or no, this is far beyond any
math I learned in school*). What made a monkey out of me was the *apparent*
simplicity. I only have a few minutes a day to work on POV, and I wasted too
many of those opportunities THINKING I had it figured out.

Either way, this is only one apparently simple piece of an apparently
simple (about 15k components) CSG construction.

 -Shay

* I learned most of my math from Povvers ABX and Tor.

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"s.day" <s.d### [at] uelacuk> wrote in message 
news:web.51f041823a6d0c04467d02b40@news.povray.org...
> The bevelling is the bit I would have most trouble with, unfortunately not 
> a
> good time for me to be attempting this but maybe in a few weeks I will 
> find some
> time to have a go, I like a challenge.

Excellent. And the bounty will stand till someone collects it.

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Am 24.07.2013 02:01, schrieb Shay:
> No blobs, SORs, isos, etc. Just the primitive primitives.
>
> Maybe I'm off my game, but this one took some head-scratching. 559
> pieces with the bounding and clipping objects.
>
> If you think you've got it figured out, try it. $50 to the POV-Ray
> wishlist (presuming this still exists) if anyone else can get it.

Maybe I'm missing something, but I come up with just 215 primitives + 69 
containers (while for some reason I don't understand POV-Ray reports 82 
finite objects and no infinite ones). Not using bounding though, which 
makes it pretty slow to render, and I have no idea why I would want to 
use clipping.

This is only proof of concept for the CSG though, with some of the 
object placement parameters just being tweaked until they fit, rather 
than having POV-Ray compute them automatically.

Ah, and of course I can't help but show off the blurred reflections 
again :-P

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Attachments:
Download 'shays_challenge.png' (531 KB)

Preview of image 'shays_challenge.png'

"clipka" <ano### [at] anonymousorg> wrote in message 
news:51f0627d@news.povray.org...
>
> Maybe I'm missing something, but I come up with just 215 primitives + 69
> containers (while for some reason I don't understand POV-Ray reports 82
> finite objects and no infinite ones).

NICE!!!!! And I'll bet it just so happens you're just the person to ask 
about that POV-team Amazon wishlist.

> Not using bounding though, which
> makes it pretty slow to render, and I have no idea why I would want to
> use clipping.

Bounding objects will account for a lot of the difference. You mentioned 
"containers"--not sure what you meant there if you didn't mean bounding.

Plus--and I'm not certain--it looks like your small-hole extrusions are 
capped with tori. Mine are slightly curved then rounded with tiny tori. If 
I'm right, there should be a difference of 24*8 objects there.

I used clipping on the tori, but that may not have been wise. You know a lot 
more about the internal workings of POV than I do.

>
> This is only proof of concept for the CSG though, with some of the
> object placement parameters just being tweaked until they fit, rather
> than having POV-Ray compute them automatically.

BOO! Close enough, though.

 -Shay

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Am 25.07.2013 02:46, schrieb Shay:

>> Maybe I'm missing something, but I come up with just 215 primitives + 69
>> containers (while for some reason I don't understand POV-Ray reports 82
>> finite objects and no infinite ones).
>
> NICE!!!!! And I'll bet it just so happens you're just the person to ask
> about that POV-team Amazon wishlist.

You'd actually have to ask Chris Cason whether that Wishlist still 
exists; I /think/ the books and hardware that were on that list have all 
been donated by now.

>> Not using bounding though, which
>> makes it pretty slow to render, and I have no idea why I would want to
>> use clipping.
>
> Bounding objects will account for a lot of the difference. You mentioned
> "containers"--not sure what you meant there if you didn't mean bounding.

containers = union, difference, intersection (and, in theory, merge; I 
didn't use that one though).

> Plus--and I'm not certain--it looks like your small-hole extrusions are
> capped with tori. Mine are slightly curved then rounded with tiny tori.
> If I'm right, there should be a difference of 24*8 objects there.

So what you are saying is that you also beveled the transition between 
the "petals" and the tori forming the end of the small-hole extrusions; 
is that the essence of it?

 From how I understand your description I suppose it should be possible 
with just 9*8 additional primitives and 3 additional containers.

> I used clipping on the tori, but that may not have been wise. You know a
> lot more about the internal workings of POV than I do.

Sounds like you used clipping as a substitute for intersection, is that 
what you're saying?

>> This is only proof of concept for the CSG though, with some of the
>> object placement parameters just being tweaked until they fit, rather
>> than having POV-Ray compute them automatically.
>
> BOO! Close enough, though.

Okay, okay - I'll try to come up with formulae for all those parameters...

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Very good indeed, except - as Shay mentioned - the tori in the holes. 
They should be curved too. That was one of my main puzzles about Shay's 
image.

Thomas

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>> No, no non-Euclidian math is needed here. One can solve the puzzle only with
>> Euclid and Pythagoras but one has to think in polar coordinates instead of
>> Euclidian ones and heavily use rotate.
>
> Isn't that non-Euclidian?

Seems like a confusion between the terms "cartesian" and "Euclidean". 
Cartesian is just a coordinate system (xyz), along with polar, 
spherical, intrinsic etc, all can be (and usually are) used with 
Euclidean geometry.

In non-Euclidean geometry essentially it it not guaranteed that two 
straight parallel lines in a plane never cross (which it is in Euclidean 
no matter what coordinate system you use to describe the lines). POV-ray 
is in no way set up to handle non-Euclidean geometry!

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