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I have an isosurface that is rolling hills based on the noise3d function.
At time increment n, I know the tangent is at pt x1,y2,z1.
At time increment n+1, I know the tangent is at pt. x2,y2,z2.
I know the distance between the two, and the time increment is so small that
I don't think I'll be harmed by assuming it's a straight line. Even with a
straight line on an inclined plane, I have no idea how the ball should
roll. The 1d & 2d solutions are trivial.
What is the rotation
Jerry wrote:
> In article <396F6E26.A9FFDE42@my-dejanews.com>,
> gre### [at] my-dejanews com wrote:
> >I've tried all kinds of tricks for 3D, and nothing looks right. The
> >problem is with a surface with a y component (rolling hills). If it
> >drops a great amount in y, it should roll more, if it drops less in y,
> >it rolls less.
>
> What you want is not how far it drops in y, but how far it rolls. That
> is, if it is rolling on a straight line, what is the length of that
> line? If it is rolling on a curve, what is the length of that curve?
>
> If the curves aren't simple circular curves (for which I think there is
> a function; perhaps the arcsin/arccos/arctan functions?), but you know
> the points anywhere on the surface (which you must, since you're putting
> the balls there?), you could approximate small triangles to get an
> approximation of the distance rolled.
>
> I wrote something about trig functions in POV
> (http://www.hoboes.com/html/NetLife/POV/Trig/) but you can probably use
> the vector functions to do what you want.
>
> Jerry
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