Path: utzoo!utgpu!watserv1!watmath!att!pacbell!pacbell.com!ames!ucsd!usc!cs.utexas.edu!chinacat!woody
From: woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal)
Newsgroups: comp.lang.postscript
Subject: Re: Bezier Interpolation
Summary: thanks, another nice ref.
Keywords: Splines, interploation
Message-ID: <1295@chinacat.Unicom.COM>
Date: 4 Jun 90 04:19:34 GMT
References: <21535@megaron.cs.arizona.edu> <7232@jarthur.Claremont.EDU> <1910@gannet.cl.cam.ac.uk>
Organization: a guest of Unicom Systems Development, Austin
Lines: 25

In article <1910@gannet.cl.cam.ac.uk>, cet1@cl.cam.ac.uk (C.E. Thompson) writes:
> 
> On the other hand, if you want the theoretical background, you can find it
> in ``Smooth, Easy to Compute Interpolating Splines'' by John D{ouglas} Hobby
> (Stanford University Report STAN-CS-85-1047, January 1985). From what
> 
> Although this is getting away from the question about splines, the theoretical
> background for many of the *other* algorithms in METAFONT can be found in
> John Hobby's PhD thesis ``Digital Brush Trajectories'' (STAN-CS-85-1070).
> 
I've given considerable thought to this problem (tracing curves), and it 
seems to me, that one can classify any 4 points in a set of data points
(provided they are close enough to a straight line), as sets of control/data
points.  Consider the subdivision spline technique.  When you have subdivided
the spline to withing your tolerance limit, you essentialy have a collection
of short splines whose control and end points (any given set of 4 points)
create an essentialy straight line.  It seems to me that it should be possible
to reverse the subdivision algo, and go back a given number of iterations, to
arrive at a set of control points, that would generate a curve that passes
through the data points.
Perhaps this is wrong, and if we have any great math guru types out here, perhaps
they could tell us if it would work or not.   It is an attractive thought,
given that the subdivision is accomplished by division by 2 (simple shifts)
Cheers
Woody