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Ron Parker wrote:
> While you're in there, add a conical component.
I've done a little bit of preliminary math on the conical blob component
idea. It shouldn't be excessively difficult to add.
The result won't look *entirely* conical, because the r function looks
like this:
r^2 = (x^2+y^2)+(1-z)^2
I think the sides of the cone, when r<1, will curve inward a little bit.
I haven't done a complete analysis of the curve; just some rough figures
on paper. Still, it ought to do.
I also did a little math on the idea of a paraboloid element; why not?
Then "r" is defined thusly:
r^2 = (x^2+y^2)+(1-z)
That one should keep more of a true shape as r gets lower.
In each of these, I think I'll need to add a way to cap off both ends,
and create a flat plane there (or really, more like the cylinder
element's cap hemispheres).
Because of that, the ideal cone would actually have a density of 1 all
through the center, but that's not possible because of the math
involved. The formula would be r^2=(x^2+y^2)/z^2 -- and since r^4 and
r^2 are both used in a fourth-order equation, things would get kind of
tricky. There'd be no real way to isolate r^2, either, and still get any
kind of a polynomial, which was my problem with the torus idea.
Gads, this stuff gets hairy....
Lummox JR
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