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I was working on my calculus when I came across this function and thought
that it would be interesting as a three dimensional rendering. I placed
spheres according to the equation and then rotated them around. There are
5796 spheres in this picture; I have tried as many as 100 000, but found
that the 'surface' did not look as good as the points. This picture took a
couple seconds to parse and about 20 seconds to render (PIII 700). I placed
a simple texture on each sphere to give it a less rendered look. I like
what came out of it, since it was so simple to make and required very little
code. I hope to find more interesting functions, and maybe try to some
truly three dimensional graphs, rather than rotating two dimensional ones.
As always any comments, good or bad, nice or mean, are welcome.
H. David Young
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Attachments:
Download 'math.jpg' (166 KB)
Preview of image 'math.jpg'
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> As always any comments, good or bad, nice or mean, are welcome.
I think it's beautiful. As a matter of fact, last time I visited home, I
almost took back one of my mother's Calculus books (she teaches high school
math) just to refresh myself on these interesting 3D functions. I would
love to see more. :)
Hershel
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Looks good...but it looks more like -x*x/(x*x - 1) to me. -x*x/x*x - 1
is the same as -1 - 1, or just -2.
An isosurface wouldn't be hard, but the radial (or circular, depending
on how you look at it) strings of spheres are interesting.
The spheres get kind of smudgy and fuzzy off in the distance...it looks
like you used focal blur, is that what causes the smudges?
Just wondering, what does this function have to do with calculus?
--
Christopher James Huff <chr### [at] mac com>
POV-Ray TAG e-mail: chr### [at] tagpovrayorg
TAG web site: http://tag.povray.org/
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It is actually: yPos = ((xPos*xPos)/((xPos*xPos)-1)), I just
said -x*x/x*x-1 to keep it simple. As for the focal blur, I didn't use
anything other than the basic shape, and a simple texture (and I think it
was the texture that caused the blur, I noticed that too). The reason I
mentioned calculus was because this was an example in my calculus text book.
The whole scene, if you are interested was:
camera {
location <1,1,-5>
look_at <0,-1.5,0>
}
light_source { <4,1,-6> rgb <1,1,1> }
light_source { <0,-1,0> rgb <.5,.2,.2> }
#declare xPos = 0;
#while (xPos < 16)
#declare yPos = ((xPos*xPos)/((xPos*xPos)-1));
#declare rot = 0;
#while (rot < 360)
sphere {
<xPos,-yPos,0>, .1
texture {
pigment {
bozo
turbulence 1
colour_map {
[0.0 rgb <.9,0,0>]
[0.5 rgb <.7,0,0>]
[1.0 rgb <.9,0,0>]
}
}
finish {
specular .2
roughness .2
}
scale .06
}
rotate <0,rot,0>
}
#declare rot = rot + 10;
#end
#declare xPos = xPos + .1;
#end
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