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From: peterf@kuling.UUCP
Newsgroups: comp.graphics
Subject: Crookedness of space-curves
Message-ID: <392@kuling.UUCP>
Date: Sat, 6-Jun-87 09:25:51 EDT
Article-I.D.: kuling.392
Posted: Sat Jun  6 09:25:51 1987
Date-Received: Fri, 19-Jun-87 01:27:46 EDT
Distribution: world
Organization: DoCS, Uppsala University, Sweden
Lines: 27

I have a problem that I would be very glad if someone could help me with:

Given a set of points in space (p1, p2,...,pn) that define a curve in 
space - is there any way of finding out how 'crooked' that curve is?

What I want is some sort of 'coefficient of crookedness' that tells me what
order I should use in a curve-drawing algorithm. The more crooked the
curve is - the higher order of the algorithm has to be used to approximate
the curve. The reason to keep the order down is that it becomes *very*
slow with high orders.


Idea: I was thinking of going through the set and for every curvesegment
defined by three points I'd solve the least-square problem,
Ax*x + Bx + C =0. Then A and B (with proper weights) would tell me how
bent all these little curvesegments are. If I add it up and divide with
the number of segments I'd have something that look like a coefficient.

If anyone has any ideas that they wish to share I'd appreciate it if you
send them to me by E-mail. To thoose of you who are also interested I'd
be glad to summarize, just mail me a note. Thanks.

-- 
==============================================================================
Peter Fagerberg             UUCP: {seismo,enea,mcvax,decwrl,...}!kuling!peterf
Applied Computer Science    ARPA: kuling!peterf@sismo.css.gov
Uppsala University          Analog: +0046 18-128286 or 8-102927