Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!texbell!chinacat!woody
From: woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal)
Newsgroups: comp.lang.postscript
Subject: Re: Bezier Interpolation
Summary: yes
Keywords: Splines, interploation
Message-ID: <1304@chinacat.Unicom.COM>
Date: 6 Jun 90 03:23:12 GMT
References: <21535@megaron.cs.arizona.edu> <7232@jarthur.Claremont.EDU> <3710@csccat.UUCP>
Organization: a guest of Unicom Systems Development, Austin
Lines: 39

In article <3710@csccat.UUCP>, larry@csccat.UUCP (Larry Spence) writes:
> In article <1295@chinacat.Unicom.COM> woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal) writes:
> >I've given considerable thought to this problem (tracing curves), and it 
> 
> Sure, but you've already stated the drawback: the data points have to
> be nearly in a straight line for this to work.  If that's the case, why not
> just approximate with a line segment?  Your approach would result in lots of
> nearly-flat Bezier segments.
> 
> Am I missing something here?

Yes.  Consider any set of control points and end points for a single spline.
The subdivision method of generating the points that are used to draw the
spline, basicaly moves the control points closer and closer to the actual
curve, and creates more and more of them.  Eventualy, when you have done
some arbitrary number of iterations, you can consider that the generated 
points define (for any single point) an endpoint and control point that
lay on the same physical spot.  You then draw a series of straight lines
between the generated points and bingo, you have a spline.  Since you
are moving the points closer and closer to the final line, it seems to me
that you could take the final line, divide it up into segments that are
an even power of 2 or whatever, and then start moving points backward, and
reducing the number of points until you got back to only 2 end points and
2 control points, at which point you should have your original control and
end points back.

Whew!.

My question, is can the subdivision method be reversed?

Cheers
Woody


> 
> -- 
> Larry Spence
> larry@csccat
> ...{texbell,texsun}!csccat!larry