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Amidst the chaos of RL, (I moved over the weekend) I managed to work out a
reliable placement of a sphere tangent to all 4 faces of any irregular
tetrahedron.
I worked out some macros to generate the determinant of a 4x4 matrix, based on
the Laplace expansion, or expansion by minors, but for whatever reason that
didn't play nicely with my tetrahedra.
I might have to shovel a lot of output to the debug stream and work out a smaple
problem by hand to see if there's a bug somewhere.
I modified some code from John Burkardt, and that seemed to work, so ...
It's immediately apparent that there will be large gaps between such spheres in
a random tetrahedral "mesh", and these guys have done some work on that next
step:
http://www.afhalifax.ca/magazine/wp-content/sciences/EmpilementDeDisques/ProducingPacking/Initialization.pdf
certainly one can see how the Delaunay-optimized triangles make the incircles
pack much more nicely, so that's a fairly important first-step to filling space
by this method.
Wondering how Ari's doing.... :D
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"Bald Eagle" <cre### [at] netscape net> wrote:
> Amidst the chaos of RL, (I moved over the weekend) I managed to work out a
> reliable placement of a sphere tangent to all 4 faces of any irregular
> tetrahedron.
> I worked out some macros to generate the determinant of a 4x4 matrix, based on
> the Laplace expansion, or expansion by minors, but for whatever reason that
> didn't play nicely with my tetrahedra.
> I might have to shovel a lot of output to the debug stream and work out a smaple
> problem by hand to see if there's a bug somewhere.
>
> I modified some code from John Burkardt, and that seemed to work, so ...
>
>
> It's immediately apparent that there will be large gaps between such spheres in
> a random tetrahedral "mesh", and these guys have done some work on that next
> step:
>
http://www.afhalifax.ca/magazine/wp-content/sciences/EmpilementDeDisques/ProducingPacking/Initialization.pdf
>
> certainly one can see how the Delaunay-optimized triangles make the incircles
> pack much more nicely, so that's a fairly important first-step to filling space
> by this method.
>
> Wondering how Ari's doing.... :D
Hi, guys! Haven't been here for a while because I am trying to find a way which
I could 'understand'.(I have found a lot of research papers on this topic but
none of them are comprehensible for me) Therefore, I ended up finish my project
*in a very simple way*. Just make random spheres and test with distance
equation. And that's it. :(
http://i.imgur.com/xH64ud9.jpg
*Dawn it! I hope I can find a way to improve the code so that they won't float*
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On 7/25/2017 7:36 PM, Ari wrote:
>> Wondering how Ari's doing.... :D
> Hi, guys! Haven't been here for a while because I am trying to find a way which
> I could 'understand'.(I have found a lot of research papers on this topic but
> none of them are comprehensible for me) Therefore, I ended up finish my project
> *in a very simple way*. Just make random spheres and test with distance
> equation. And that's it.:(
> http://i.imgur.com/xH64ud9.jpg
> *Dawn it! I hope I can find a way to improve the code so that they won't
> float*
>
>
Good of you to come back. :)
I said at the beginning that it was not trivial. I wonder what your
lecturer's solution would be?
Your image looks a good solution but you are an Engineer. What were your
tolerances?
Now you know your way here. Don't be a stranger. :)
--
Regards
Stephen
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> > Hi, guys! Haven't been here for a while because I am trying to find a way which
> > I could 'understand'.(I have found a lot of research papers on this topic but
> > none of them are comprehensible for me)
*** Yet *** ;)
> Therefore, I ended up finish my project
> > *in a very simple way*. Just make random spheres and test with distance
> > equation. And that's it.:(
> > http://i.imgur.com/xH64ud9.jpg
> > *Dawn it! I hope I can find a way to improve the code so that they won't
> > float*
Excellent. It's important to stick with it and DO _something_, even if it's not
ideal. Never let the perfect be the enemy of the good.
I like your results.
Now you know more about how "the devil is in the DETAILS", and it's NEVER _just_
"All you have to do is..."
As a computer graphics trick, why don't you try increasing the size of all those
rocks by 10, and then take the whole thing and scale it by 1/10.
The apparent size of the rocks might stay the same, while the spaces between
them that make them look like they're floating (because they are) might be
reduced by 9/10.
If that works, try doing the same with 100 or 1000 instead of 10.
> I said at the beginning that it was not trivial. I wonder what your
> lecturer's solution would be?
If it's an engineering class, he might not have one - it might be an open-ended
exercise to see what people come up with.
> Now you know your way here. Don't be a stranger. :)
Indeed, there's always more fun to be had, and so very many things to learn.
Check out:
https://malbertsinvention.wordpress.com/2013/08/15/realistic-dry-stone-wall-physics-test/
https://www.google.com/search?q=rocksolver
https://www.google.com/search?q=robot+arm+stack+stones
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> Good of you to come back. :)
>
> I said at the beginning that it was not trivial. I wonder what your
> lecturer's solution would be?
There is no solution :( The professor just wanted to let us try something *new*
and see if we are interested in this software. Overall, I think this software is
pretty fun. I think I will come back after attending more math class in the
University :D.
>
> Your image looks a good solution but you are an Engineer. What were your
> tolerances?
>
Same as the above. We don't have any 'standard' or 'marking scheme'. My
professor just found out that amazing grains picture and he told us it could be
a great example for us to begin with and imitate. So, I need to figure out how
to render a similar scene :D.
> Now you know your way here. Don't be a stranger. :)
Ayyyyy, thank you Stephen B-).
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> Excellent. It's important to stick with it and DO _something_, even if it's not
> ideal. Never let the perfect be the enemy of the good.
That's true! Trying to be *perfect* is actually the culprit of my anxiety. After
I changed from *perfect mode* to *good mode*, I started to appreciate this
software. What a great invention :D.
> I like your results.
> Now you know more about how "the devil is in the DETAILS", and it's NEVER _just_
> "All you have to do is..."
>
> As a computer graphics trick, why don't you try increasing the size of all those
> rocks by 10, and then take the whole thing and scale it by 1/10.
> The apparent size of the rocks might stay the same, while the spaces between
> them that make them look like they're floating (because they are) might be
> reduced by 9/10.
That's cute :P. I think I will try it later.
> If that works, try doing the same with 100 or 1000 instead of 10.
>
>
> > I said at the beginning that it was not trivial. I wonder what your
> > lecturer's solution would be?
>
> If it's an engineering class, he might not have one - it might be an open-ended
> exercise to see what people come up with.
Yes, it is. :D
>
> > Now you know your way here. Don't be a stranger. :)
>
> Indeed, there's always more fun to be had, and so very many things to learn.
>
> Check out:
>
https://malbertsinvention.wordpress.com/2013/08/15/realistic-dry-stone-wall-physics-test/
> https://www.google.com/search?q=rocksolver
> https://www.google.com/search?q=robot+arm+stack+stones
They are some interesting examples, especially the robot one. The Rocksolver is
great, too! Thank you so much B-).
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Just found this while looking for something else:
http://www.hib-wien.at/leute/wurban/informatik/osculating/index.html
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Related threads, re: placing non-intersecting spheres:
http://news.povray.org/povray.windows/thread/%3Cweb.47841f263bacf7e1748549bc0%40news.povray.org%3E/?mtop=257707&moff=10
http://news.povray.org/povray.binaries.images/thread/%3C4468e90a%40news.povray.org%3E/?ttop=257697&toff=1000
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Somewhat related.
Nice little render. Doesn't seem like they avoid overlapping.
Interesting method / approach.
http://louisbel.free.fr/scenes/scene002.shtml
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Placing these here for future reference:
http://news.povray.org/povray.general/thread/%3Cweb.4c6830857e94b25d7fd0e21e0%40news.povray.org%3E/?mtop=350012&moff=10
http://wiki.povray.org/content/User:Edouard
https://www.youtube.com/watch?v=flQgnCUxHlw&list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH&index=37
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