Don is a tough guy to help. He is very sharp, so when he asks a question he already has a good understanding of the topic. But he doesn't know how to discuss a topic worth a hoot. I think he is the sort of designer who doesn't understand people so well and has trouble putting himself in your position.
This thread contains many great examples of how he fails to connect the dots of communication. Most notable he has never explained the form of the solution he is looking for. He asks for a way to "characterize (describe) the curve" without adequately explaining what "characterize" means all because he doesn't grasp what others fail to understand about his "technically" correct question.
I remember in college a student would ask a question but not convey his real point of confusion to the professor. Understandable, since he is lacking knowledge of the topic. But the professor would often fail to get what the question was really about. Sometimes this would be so obvious to me that I would raise my hand and explain it for him. lol Not much I can do to help Don though. It has been a long time since I worked with Bezier curves. Reading about them briefly doesn't give me a
be "characterized". But I can see a small start. It should be easy to obtain the slope of the line at the end points. I don't know, but I suspect it should be possible to determine if the curve has a loop or not.
I expect if he asked his question in a more math oriented group he would find an answer. This group has a lot of sharp people, but many of them are admittedly rather math challenged. Perhaps the comp.dsp group would be better, but I am sure they will want a reasonable definition of "characterize" before they will even start on an answer.