Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!wuarchive!texbell!uudell!bigtex!natinst!rpp386!woody
From: woody@rpp386.cactus.org (Woodrow Baker)
Newsgroups: comp.lang.postscript
Subject: Re: Splines Underli
Summary: yup
Message-ID: <17833@rpp386.cactus.org>
Date: 1 Feb 90 05:17:53 GMT
References: <7897@shlump.nac.dec.com> <17811@rpp386.cactus.org> <1990Jan31.213001.11641@intercon.com>
Organization: River Parishes Programming, Plano, TX
Lines: 33

In article <1990Jan31.213001.11641@intercon.com>, amanda@mermaid.intercon.com (Amanda Walker) writes:
> In article <17811@rpp386.cactus.org>, woody@rpp386.cactus.org (Woodrow Baker)
> writes:
> > The little spline routine that was sent to me, was much appreciated.
> > Now, a followup question.  Given the resulting array of points, 
> > created by the subdivision of the spline, is is possible to reverse the
> > proceedure, and work back to the original set of corrdinates.  If so,
> It should be possible, since four points will uniquely define a cubic
> curve.  It's been a while since I took Analytic Geometry :-), but you
> should be able to take four points on the curve, spaced as equally as
> possible to assure maximum accuracy, and write four equations in four
> unknowns (one for each point, with the unknowns being the coefficients
> of the cubic), which you can then solve using Gaussian elimination or
I have been working on this problem for a while.  I have arrived at using
a Gauss-Jordan elimination.  I still have not got it implemented.  I
recieved a snippet of 'C' code, that took 2 endpoints and 2 control points
and by subdividing the spline recursively until an arbitrary tolerance
limit was reached, resulted in an array of coordinates that when plotted
draws the spline.  My question concernes taking that array, and working
it backward through the mirror of the subdivision, and coming to the
original points.  The subdivision code was implemented by shifting
in order to divide by 2.  Can a mirror function be readily created such
that when passed the array of points, (always a multiple of 2 long),
you can reconstruct the original 4 sets of points?  I am not sure
that a Gauss Jordan curve fitter would be the most effecient way to do
this.  Any ideas anyone?  
p
PS, thanks for the post...
Cheers
Woody
> 
> "Many of the truths we cling to depend greatly upon our own point of view."
> 	--Obi-Wan Kenobi in "Return of the Jedi"