Hi Folks, rc explained his path approximation problem. >My needs are...take scanned points and approximate them closely with >a curve, reducing the number of points needed to describe the area,... I'm not sure we have the right leads yet. Since spline approximation for font creation and vectorization has been a major programming activity so there has to be a lot of good stuff out there though most of it is occulted by copyright and patents. Let me mention a few mountains on my horizon. 1) 'TeXtrace' by Peter Szabo and 'autotrace' Martin Weber (see their sites via Google) involve a high performance solution to **exactly** rc's problem. Some neat pictures. But I was unable to find a conceptual explanation there of algorithms. Tell me if you do. 2) Knuth's metafont program involves an excellent solution to half of rc's problem: Given a sequence of points in the plane, find the "most beautiful" geometrically smooth cubic spline curve that passes through all of them in order. The algorithm is found in John Hobby's thesis (under Knuth direction) and there is a preprint for the published version on Hobby's site at Lucent. (a) the results are brilliant and give the finest algo in Knuth's metafont. You can enjoy the solutions by getting OzTeX from the CTAN archive, which includes a variant if metafont called matapost (by Hobby) which has PS and PDF output. (b) although the technical details are daunting (and maybe not optimal?) there is a clear idea behind the algorithm which is in fact an intelligent interpretation of the mechanics of a spline as used in the loft of a pre-computer naval architect (originally, a spline was a long, thin, flexionally elactic, smooth, wooden stick or plank). The mathematical quantity Hobby minimizes is something like the integral of a high (fourth?) power of curvature suitably normalized. That process tends to even out curvature eliminating gratuitous bumps. It would be very nice to have an clear explanation that allows an elegant computer implemetnation, for example by monte-carlo methods. Our computers are more than adequate to simulate that sort relaxation of a combinatorial spline. So that's a vague idea for a Hobby's nice solution of half the problem. Maybe Szabo or Weber understand better, but just as likely they have simply gotten their hands on a portable C-library that implements these ideas (and more). Tell us what you find. Cheers Laurent S. PS. Does Quickdraw include a API offering at least b'zier curves readymade???