"TC" wrote:
> Do you have any idea how to approach the complex modeling required for your
> kind of beveled surfaces using isosurfaces? Does anybody in this newsgroup?
> (Non rhetorical question - if anybody does, please tell.)
>
If you can assume the bevel has tighter curvature than surfaces of the objects
being joined, it should be just a matter of restricting the second derivative
(curvature) of your approximation function in that region to fall within the
desired beveling range.  In other words, if your object surfaces have a minimum
radius of curvature of, let's say, one unit, and you want a bevel radius of
about 0.1 units, limit your isosurface approximation to have a second derivative
resulting in a minimum curvature radius of 0.1.

I'd have to work out the math to verify this, but intuitively this should be a
matter of limiting the isosurface's second partial derivatives to all be less
than the inverse of the desired bevel curvature, 10 in this example.  I have a
hunch that this requirement will carry through fairly cleanly to an algorithm
used to determine an approximating function, but probably don't have time to
pursue it further at present.

Unfortunately, I have to put this problem on my stack of things I'd rather do
than what those paying my tuition want to see (which also has to do with
numerical differentiation and integration).

But I hope this helps a bit.

David Wagner

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