Path: utzoo!attcan!uunet!mcsun!ukc!slxsys!dircon!uad1077
From: uad1077@dircon.uucp
Newsgroups: comp.lang.postscript
Subject: Re: Bezier Interpolation
Keywords: Splines, interploation
Message-ID: <1990Jun6.180021.13742@dircon.uucp>
Date: 6 Jun 90 18:00:21 GMT
References: <7232@jarthur.Claremont.EDU> <1910@gannet.cl.cam.ac.uk> <1295@chinacat.Unicom.COM>
Organization: The Direct Connection, UK
Lines: 22

> 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.


No, it doesn't work that way.  The reason cubic curves have 4 controls 
is because you have to completely specify 4 coefficients in the cubic 
polynomial that gives the curve.  If you glue two cubics together, then 
you have 8 controls (although there may be constraints introduced by
whatever order of continuity you are interested in), but that does
mean that you get a 7th-order polynomial as a result.  YOu are now
faced with the problem of approximating a 7th-degree polynomial with
a cubic, which is harder than the original problem of apporximating
a set of data points with a cubic, before you can proced to the next
stage of `unsubdivison'.  I agree though: like much of numerical work,
it IS a pity!
-- 
Ian D. Kemmish                    Tel. +44 767 601 361
18 Durham Close                   uad1077@dircon.UUCP
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