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From: bdd@calmasd.Prime.COM (Brian Donahue)
Newsgroups: comp.graphics
Subject: Re: Curve through 3 points
Message-ID: <1672@calmasd.Prime.COM>
Date: 15 Aug 90 19:13:06 GMT
References: <1990Aug13> <23900010@sunb5> <MONTNARO.90Aug15121325@spyder.crd.ge.com>
Organization: Calma - A Division of Prime Computers
Lines: 37

>In article <23900010@sunb5> mcooper@sunb5.cs.uiuc.edu writes:
>
>   look under "Bezier Curves" in any graphics textbook 
>   (Foley &VanDam come to mind)
>
>Bezier curves have several nice properties, including local spline control,
>the control points form a convex hull for the spline, and the ability to
>easily make successive chunks piecewise continuous, but they don't
>interpolate their control points. That make them more difficult to use
>interactively, since the curve generated is not immediately obvious from the
>control points.
>
By now, I've forgotten what the original poster wanted, but s/he might
try parabolas in the Bezier format.  For a crv through the 3 points
(P0, P1, and P2), the bezier quadratic that 'fits' that data 
looks something like:

		C1
		*

		*
		P1

	*	*	*
	P0	m	P2
	C0		C2

where C0,C1, and C2 are control points (C0=P0, C2=P2, and P1 = (m+C1)/2
where m = (P0+P2)/2..)  Look at "The twisted cubic curve: a CAGD approach"
A.R. Forrest, CAD vol. 12, #4, july 80 for more on bezier/conics.

'course, if you wanted arcs, or wanted to string continuous curves thru
more than 3 points, you've got more work to do...:-)

good luck,
bd
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