On Oct 7, 2006, at 10:45 AM, Lars Jensen wrote:
Note that creating a texture that fits this triangle is not at all
trivial to produce. Once the proportions for the texture is found,
the texture's size would need to be basically doubled in order to get
the equivalent resolution of a square particle.
>SNIP< but consider this picture:
It shows your texture with a triangle that encloses most of the good
stuff. The triangle probably has even less area than the original
square. But the texture that encloses the triangle has roughly twice
the area of the original square. Is that what you mean by "basically
doubled"?
Hmm. Now that I see my own response, I may have confused things a
bit. Bear with me while I talk out loud a bit:
I simplified my assumptions even further than what you've drawn.
First treat the particle image as a round circle rather than an odd
shape (that's what I did to build that spark texture). Next, draw a
triangle around it which will fit that shape, making sure that
triangle is vertically symmetrical. This will guarantee you a good
fit for any round-shaped particle texture.
For a more concrete example: in Meshwork (Joe Strout's 3DMF modeling
app at <http://www.codenautics.com/meshwork/>), create a sphere
centered at the origin (use the default 100-unit diameter). Now
create a triangle shape around that area which encompasses the entire
sphere. That triangle will probably be close to an equilateral
triangle that is symmetrical around the Y-axis, the bonus part of
which that its vertex coordinates will allow the particle to spin
perfectly about the center. You'll probably find that the width of
the triangle's base to be about 200 units.
Now if you take that 200 units and draw a box around that with a
width and height of 200 units, visually the triangle is roughly half
the size in area of the square. This is what I used to say that your
texture size must be doubled to match the equivalent square. See
diagram at <http://www.jcquan.com/RB/TriangleParticles.png>
My mistake in the UV coordinates I sent out earlier is not burning
them in with the square. That would allow the dimensions of the
particle texture to remain a ratio of 1:1.
In other words: In Meshwork, select everything (sphere, triangle,
box) and in whichever material you choose, click planar mapping and
click the Set button to lock in the planar UV coordinates. Close that
material's window and re-open it, setting the mapping to pinned. If
you now delete the sphere and box, you now have the UV coordinates
for the triangle which you can use in the demo app. Oh, and you might
want to reduce the dimensions of that triangle to unit size before
dropping it in the demo app.
The above example works for a round texture, but as soon as you want
to do a texture that's wider than tall (or vice versa), you'll need
to bump up that texture resolution. This is where the square particle
does better damage control (so to speak), allowing more freedom for
oddly-shaped textures.
I'm running entirely by visual examples here. Feel free to let me
know if there's something flawed with my reasoning -- I'd like to
learn along with everyone else!
==
Jeff Quan
jquan at mindspring dot com
http://www.jcquan.com/JQportfolio
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