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Spiral isosurface II by Mershell Spiral isosurface II by Mershell
Once again, lack of a good title.
Four isosurfaces, in pairs that are 180 degrees out of phase. Nothing in this scene modeled by hand, it's all equations that I spent forever working with.

For the curious and mathematically oriented:
f(x,y,z) = sqrt((ay - b sin(cx + d))^2 + (az - b cos (cx + d))^2) . . . . a and b are...uhh...something with radius, c is frequency, d is phase. It's pretty straightforward: the parametric equation for a 3D spiral is (u, sin(u), cos(u)); add in some functional transforms and apply the distance formula. The intention was that I would get a sphere sweep as a result of using the distance formula, but that didn't work out.
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Mershell Featured By Owner Jul 5, 2005   Digital Artist
Yeah, it's POV-Ray 3.6.1, on my flashy new computer that can render a LOT faster than a $15 dumpster Celeron. But, alas, that $15 computer died in the middle of the night and I smashed it very violently.
The equation part may not make sense until you read about how isosurfaces work, in POV-Ray or otherwise... you have a function of 3 variables, and it will have a value for any point in the 3D space... if the function evaluated at a point is equal to a certain threshold, the point is on the surface; if less than, it's outside; if greater than, it's inside.
The parametric equation (u, sin(u), cos(u)) gives a simple helix along the X axis - but it's just a 2D line wrapped around and around, basically. To get anywhere, you need to get some kind of value for any point in 3D space. So... take my oddball approach... and use the distance formula to find the distance between the given point and whatever part of the spiral happens to have the same X coordinate. Why this works, I'm not sure.
Not explained well enough? Probably not, I don't know what I'm talking about beyond this.
parrotdolphin Featured By Owner Jul 16, 2005  Professional Digital Artist
Smashed your computer in the middle of the night? Hee hee, sounds like fun. I'm not much of a math genius these days, been a LONG time, but thank you for the explanation. I'd love to see what the POV-Ray program looks like, if you'd like to share it. If not, that's cool too. =p But, I will check out isosurfaces in POV-Ray. Maybe I'll even get somewhere with it.
dawncrow Featured By Owner Jul 5, 2005   Photographer
Holy crap. I don't get the equation part, but the spiral looks pretty sweet.
parrotdolphin Featured By Owner Jul 5, 2005  Professional Digital Artist
Very cool! Did you use POV-Ray to make this?
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Submitted on
July 5, 2005
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