POV-Ray : Newsgroups : povray.binaries.animations : Re: Marbles : Re: Marbles Server Time
19 Jul 2024 02:15:15 EDT (-0400)
  Re: Marbles  
From: Chris Johnson
Date: 1 Oct 2003 15:43:28
Message: <3f7b2e60@news.povray.org>
-[how do you calculate interaction between two parabels?]-
If the parabolas have the same curvature (e.g. same acceleration downwards due to
gravity), the
objects will be in straight lines moving relative to each other, so the straight line
code will do.

Just on the back of an envelope (literally) I think I've got the general idea of
parabola
interstections with accelerations that aren't the same - I haven't checked it yet. If
you subtract
one parabola quadratic from the other to get a parabola of relative motion. This then
intersects a
circle, representing the sum of the radii. The parabola can be shifted to make the
circle lie on the
origin, i.e.



this gives a quartic, which can be solved exactly, but its a bit more difficult than a
quadratic. A
quartic makes sense, because there can be up to four intersections of the parabola
with the circle
(e.g. something like 100-1000x^2 and r=50)

I haven't worked the details of this one out yet - I think the values of a, b, c and d
are likely to
be fairly long expressions in themselves.

-Chris


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