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Folks:
Fiddled about a bit more with tiles last night
and came up with this work-in-progress.
Aaron
Aaron Gillies
New York City
xerxes[^]yahoo.com
Post a reply to this message
Attachments:
Download 'success.jpg' (44 KB)
Preview of image 'success.jpg'
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And here is one that samples a bitmap for the pigment
pattern. It's not as successful as the previous one,
since the tiles are too large at present to make the
image in the mosaic discernable.
Aaron
Aaron Gillies
New York City
x3rxes[&]yahoo.com
Post a reply to this message
Attachments:
Download 'success.jpg' (47 KB)
Preview of image 'success.jpg'
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Thats pretty amazing Aaron, how do you get tiles to line an arbitrary
surface like that? And with a pattern no less?
George
"Aaron Gillies" <no### [at] spam com> wrote in message
news:3E1### [at] spamcom...
> Folks:
>
> Fiddled about a bit more with tiles last night
> and came up with this work-in-progress.
>
> Aaron
>
> Aaron Gillies
> New York City
> xerxes[^]yahoo.com
>
----------------------------------------------------------------------------
----
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It's a bit complicated to explain, and my code is so
terrible that I don't dare post it. Briefly, I thought
of the problem as lining the interior of a dome with
rows of tiles. So, I used trigonometry to calculate
the X and Y position of one endpoint of each row and
then rotated the tiles around the Y axis. The number of
tiles in each row was calculated by taking the
circumference of the circle defined by the end points
and dividing it by the size of the tile. I then
rotated each tile to the proper angle. Seems like
a lot of work for just this effect and I wonder if
there is not an easier way ...
Aaron
Aaron Gillies
New York City
x3rxes[^]yahoo.com
George Pantazopoulos wrote:
> Thats pretty amazing Aaron, how do you get tiles to line an arbitrary
> surface like that? And with a pattern no less?
>
> George
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Hey Aaron,
What if you used the spherical coordinates ( rho, phi, theta ) in a
nested loop? Theta is the angle corresponding to the floor of the dome. Phi
is the other angle, a *quarter-circle* going from the tip of the ceiling to
the
floor. It shouldnt matter if you increment phi or theta in your inner loop,
you'd just use the remaining one as the outer loop and increment it there.
Theta would go from [0 to 2PI] and phi would go from [0 to PI/2], and
rho would be a constant (the radius of the dome). You would use a timestep t
and place a tile at every timestep in your inner loop (as well as increment
the angles). To actually place the tile, you would convert from spherical to
rectangular coords as follows:
x = rho sin (phi) cos ( theta )
y = rho sin (phi) sin ( theta )
z = rho cos (phi)
Just an idea, this would elegantly accomplish what you did in a loop.. I
just took Calculus 3, and this is basically how we integrate a multivariable
function in spherical coordinates.
Regards,
George Pantazopoulos
"Aaron Gillies" <no### [at] spamcom> wrote in message
news:3E1### [at] spamcom...
> It's a bit complicated to explain, and my code is so
> terrible that I don't dare post it. Briefly, I thought
> of the problem as lining the interior of a dome with
> rows of tiles. So, I used trigonometry to calculate
> the X and Y position of one endpoint of each row and
> then rotated the tiles around the Y axis. The number of
> tiles in each row was calculated by taking the
> circumference of the circle defined by the end points
> and dividing it by the size of the tile. I then
> rotated each tile to the proper angle. Seems like
> a lot of work for just this effect and I wonder if
> there is not an easier way ...
>
> Aaron
>
> Aaron Gillies
> New York City
> x3rxes[^]yahoo.com
>
>
> George Pantazopoulos wrote:
> > Thats pretty amazing Aaron, how do you get tiles to line an arbitrary
> > surface like that? And with a pattern no less?
> >
> > George
>
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George:
I get what you are saying. I guess I should hit
the math textbooks again and figure this out. Any
interest in putting together a demo scene that
does what I did using spherical coordinates?
I had a semester of Calculus in college, ten years ago ...
Downloading an old Trig textbook in PDF format
yesterday was a big adventure for me.
Aaron
Aaron Gillies
New York City
x3rxes[*]yahoo.com
Post a reply to this message
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I think that would be a fun thing to do, I'll try when I get some time,
either today or later this week. Congrats on refreshing your math skills, it
will help a lot :)
George
"Aaron Gillies" <no### [at] spamcom> wrote in message
news:3E1### [at] spamcom...
> George:
>
> I get what you are saying. I guess I should hit
> the math textbooks again and figure this out. Any
> interest in putting together a demo scene that
> does what I did using spherical coordinates?
>
> I had a semester of Calculus in college, ten years ago ...
> Downloading an old Trig textbook in PDF format
> yesterday was a big adventure for me.
>
> Aaron
>
> Aaron Gillies
> New York City
> x3rxes[*]yahoo.com
>
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3E1### [at] spamcom...
> It's a bit complicated to explain, and my code is so
> terrible that I don't dare post it.
It's more or less the same technique as the one used here
http://www.oyonale.com/ldc/images/arene.jpg
Took me a while to figure it out though. The main problem is that one can't
prevent bricks or tiles to be perfectly aligned one above each other once in
a while, which doesn't make sense in architecture... It's not a problem for
mosaics of course and with the proper mosaic texturing the results are
indeed nice.
G.
--
**********************
http://www.oyonale.com
**********************
- Graphic experiments
- POV-Ray and Poser computer images
- Posters
Post a reply to this message
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"George Pantazopoulos" <the### [at] attbicom*KILLSPAM*> wrote
> x = rho sin (phi) cos ( theta )
> y = rho sin (phi) sin ( theta )
> z = rho cos (phi)
>
> Just an idea, this would elegantly accomplish what you did in a loop.. I
> just took Calculus 3, and this is basically how we integrate a
multivariable
> function in spherical coordinates.
That won't work to accomplish a good enough equidistant distribution. To see
why, consider the case where phi=0. You'll get stacked tiles at x=y=0, and
not enough tiles, say, at phi=Pi/2.
Post a reply to this message
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> So, I used trigonometry to calculate
> the X and Y position of one endpoint of each row and
> then rotated the tiles around the Y axis. The number of
> tiles in each row was calculated by taking the
> circumference of the circle defined by the end points
> and dividing it by the size of the tile. I then
> rotated each tile to the proper angle. Seems like
> a lot of work for just this effect and I wonder if
> there is not an easier way ...
Perhaps there is... you should post the comp.graphics.algorithms and see if
anyone can come up wit something?
It doesn't matter how good or bad your coding might be as long as it works
really. I think it appears to do the job very well.
Now what about the cylinder? For that matter what about other shapes inside
or out? If you get that down then you have some real possibilities.
Automatic mosiacs or tiling inside a cylindrical rendered bathroom. Might
be a neat tool to have! :)
Cone might be the trickiest to do I think. Of the primitives that is.
---
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