Re: [help-3dldf] Intersections of NURBs

[L. Nobre G.]

On Fri, 28 Jan 2005, Laurence Finston wrote:

> I hope nobody considers this question off-topic on the MF
> and MP lists.

I don't but I leave to you the posting of this reply on the MF and MP
lists.

> Shapes defined by arbitrary curves are
> a bigger problem.

Do you mean "arbitrary surfaces"?
If the awswer is "no", stop reading.

> "Decomposing" requires finding the intersections of
> a given pair of objects.

Supposing one has found one point where two arbitrary parametric surfaces
of degree greater then 2 intersect I'd go for a "continuation method" to
run over the intersection curve. It is somewhat similar to
numerically solving a differential equation (or finding a contour line).

> I've taken a look at Knuth's method of finding
> intersections, but it appears to depend on the limited
> precision whole-number arithmetic he uses, and is thus not
> applicable to my more conventional approach using `floats'
> or `doubles'.

One can cast floats and doubles into limited precision...

> I'm not expecting this to be easy, but any hints would be
> much appreciated.

I don't know NURBS but, maybe, there is a standard way to
calculate the polyhedric control surface of surface-NURBS.
If this polyhedric control surface exists, calculating the intersection of
two arbitrary surfaces reduces to finding the piece-wise linear
intersection of two polyhedric surfaces and then `converting' this
polyline to a line-NURBS. Maybe, this convertion is possible and maybe, it
produces the correct intersection. Well, maybe, maybe...

Lu\'{\i}s Nobre Gon\c{c}alves - http://matagalatlante.org