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Hi all...
recently I was confronted with a bit of a brain teaser: When a cube is spun
about the axis of it's two opposite corners what is the shape of the space
it passes through?
I had a few bright idea's.. some of them pretty accurate.. but before long I
decided to test the result.
The resulting shape is fairly intriguing so I thought it may be worth
sharing.
BTW.. just try placing a POV cube so that two opposite corners lie on the y
axis. It's trickier than it sounds.
--
Ian
Inkwell: Ian's Homepage
http://www.topcities.com/cartoon/inkwell/index.htm
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Attachments:
Download 'rypic.jpg' (110 KB)
Preview of image 'rypic.jpg'
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A kind of amusement park carousel ride object. If you make that with filtered
color and give it a ior I'd bet it would take 100 times longer to render, if
not more :-)
Bob
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Looks like a circus tent...
And is that one of my post_process filters you used to make the circular
image? Maybe multiply and add with a spherical/wood/onion/cylinderical
pigment?
--
Christopher James Huff - Personal e-mail: chr### [at] mac com
TAG(Technical Assistance Group) e-mail: chr### [at] tagpovrayorg
Personal Web page: http://homepage.mac.com/chrishuff/
TAG Web page: http://tag.povray.org/
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Chris Huff <chr### [at] maccom> wrote in message
news:chrishuff-EF9A5B.12173503072000@news.povray.org...
> Looks like a circus tent...
> And is that one of my post_process filters you used to make the circular
> image? Maybe multiply and add with a spherical/wood/onion/cylinderical
> pigment?
No, I used Adobe Photodeluxe... I guess I can't enter this in the irtc :-)
--
Ian
Inkwell: Ian's Homepage
http://www.topcities.com/cartoon/inkwell/index.htm
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Ian Witham <ian### [at] hotmailcom> wrote:
: BTW.. just try placing a POV cube so that two opposite corners lie on the y
: axis. It's trickier than it sounds.
It requires some math.
One may think that just rotate 45 degrees around x axis and then 45 degrees
around z axis, but one will soon discover that it's not so easy (when trying
to render it).
The first step was right: rotating 45 degrees around the x axis makes the
diagonal to lay on the x-y plane. Now we only need to rotate it around the
z axis so that the diagonal is parallel to the y axis.
The reason why 45 degrees is not correct is because the diagonal
is not 45 degrees from the y axis anymore. This is because now the diagonal
is higher than it's wide.
More precisely the diagonal is 2*1 units wide while it's 2*vlength(<1,1,0>)
units high (supposing we have a -1,1 cube).
The degree is precisely asin(width/length), ie. asin(1/vlength(1,1,1)).
Now we only have to translate the box up so that the corner will be located
at the origin. Since we have the length of the diagonal (2*vlength(<1,1,1>)),
that's easy.
In povray code it will be:
camera { location <-2,4,-10> look_at y angle 35 }
light_source { <100,200,-300> 1 }
plane { y,0 pigment { checker rgb 1, rgb .5 } }
box
{ -1,1 pigment { rgb <1,1,0> }
rotate x*45
#declare len = vlength(<1,1,1>);
rotate z*degrees(asin(1/len))
translate y*len
}
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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Ian Witham wrote:
> Hi all...
> recently I was confronted with a bit of a brain teaser: When a cube is spun
> about the axis of it's two opposite corners what is the shape of the space
> it passes through?
Ooh, sounds easy...
> BTW.. just try placing a POV cube so that two opposite corners lie on the y
> axis. It's trickier than it sounds.
Bah, rotate <0,45,degrees(asin(1/sqrt(3)))-90> should do it.
Okay, i'll stop ;)
--
David Fontaine <dav### [at] faricynet> ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/
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On Tue, 4 Jul 2000 04:36:38 +1200, Ian Witham wrote...
> Hi all...
> recently I was confronted with a bit of a brain teaser: When a cube is spun
> about the axis of it's two opposite corners what is the shape of the space
> it passes through?
> I had a few bright idea's.. some of them pretty accurate.. but before long I
> decided to test the result.
> The resulting shape is fairly intriguing so I thought it may be worth
> sharing.
> BTW.. just try placing a POV cube so that two opposite corners lie on the y
> axis. It's trickier than it sounds.
You could have just asked what a spun cube looked like. Anyone who's
ever played roleplaying games (AD&D (Yech!), Call Of Cthulhu, Runequest,
etc.) and gotten bored would have been able to tell you that the answer
is a SOR with a profile of a sort of waisted equilateral diamond.
Well, that made no sense. Go find a six sided dice, and spin in on a
flat surface. It'll probably take a hell of a lot longer than it took
you to do the maths, write the scene file and render it...
<grin>
Oh, and I figured it out using a pencil, paper and calculator, and the
rotations I came out with were <45.0,0.0,35.26439>. This was using
nothing more complicated than basic trigonometry and Pythagoras' theorem.
Bye for now.
Jamie.
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Jamie Davison wrote:
> <grin>
>
> Oh, and I figured it out using a pencil, paper and calculator, and the
> rotations I came out with were <45.0,0.0,35.26439>. This was using
> nothing more complicated than basic trigonometry and Pythagoras' theorem.
<grin>
*cough cough*
I will not tolerate imperfection! Rotate <45,0,asin(1/sqrt(3))> ;-)
--
David Fontaine <dav### [at] faricynet> ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/
Post a reply to this message
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> Oh, and I figured it out using a pencil, paper and calculator, and the
> rotations I came out with were <45.0,0.0,35.26439>. This was using
> nothing more complicated than basic trigonometry and Pythagoras' theorem.
okay okay.. as so many of you have pointed out it isn't all that tricky
after all <hangs his head in shame> :-(
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Ian Witham wrote:
> okay okay.. as so many of you have pointed out it isn't all that tricky
> after all <hangs his head in shame> :-(
Wait, wait, I have a *really* hard one! What would it look like if you took a
regular octahedron, aligned opposite points on the y-axis, and spun it? Only
kidding, of course... (not to self--shut up)
--
David Fontaine <dav### [at] faricynet> ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/
Post a reply to this message
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