[metapost] Re: all intersections between two paths

[Laurence Finston]

Larry Siebenmann wrote:

> LF> My specific challenge is implementing routines for finding
> LF> intersections of arbitrary three-dimensional Metafont-like
> LF> `paths' in GNU 3DLDF.
> 
> Are these generalized paths allowed to have dimension 2, ie to
> be surface patches?  Any degrees >3 badly wanted?
> 

Actually, I just took the opportunity to pose my question because the subject
had come up.  While I am interested in the answer, my more immediate concern
is finding the intersections of non-arbitrary paths, such as straight lines,
polygons, ellipses, circles, hyperbolae, etc.  
I hope for an improvement in performance from implementing NURBs, but they
won't bring an improvement in the way curves are rendered.  I can get equally
good results by just using more points on a given path.  The advantage to
using NURBs would be that I wouldn't have to project so many points. 
Therefore I've decided that my next task will be to work on surface hiding
with non-arbitrary paths.   NURBs are, of course, interesting in their own
right.

I do eventually want to implement surface patches and n-dimensional
geometrical figures for all n.

Laurence