From: ferdinan@oeinck.waterland.wlink.nl (Ferdinand Oeinck)
Subject: Re: detecting double points in bezier curves
Organization: My own node in Groningen, NL.
Lines: 34

renner@adobe.com (John Renner) writes:

> In article <19930420.090030.915@almaden.ibm.com> capelli@vnet.IBM.COM (Ron Ca
> >In <ia522B1w165w@oeinck.waterland.wlink.nl> Ferdinand Oeinck writes:
> >>I'm looking for any information on detecting and/or calculating a double
> >>point and/or cusp in a bezier curve.
> >
> >See:
> >   Maureen Stone and Tony DeRose,
> >   "A Geometric Characterization of Parametric Cubic Curves",
> >   ACM TOG, vol 8, no 3, July 1989, pp. 147-163.
> 
> I've used that reference, and found that I needed to go to their
> original tech report:
> 
> 	Maureen Stone and Tony DeRose,
> 	"Characterizing Cubic Bezier Curves"
> 	Xerox  EDL-88-8, December 1988
> 

First, thanks to all who replied to my original question.

I've implemented the ideas from the article above and I'm very satisfied
with the results. I needed it for my bezier curve approximation routine.
In some cases (generating offset curves) loops can occur. I now have a
fast method of detecting the generation of a curve with a loop. Although
I did not follow the article above strictly. The check if the fourth control
point lies in the the loop area, which is bounded by two parabolas and
one ellips is too complicated. Instead I enlarged the loop-area and
surrounded it by for straight lines. The check is now simple and fast and
my approximation routine never ever outputs self-intersecting bezier curves
again!
Ferdinand.

