Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!apple!sun-barr!ames!sgi!robert@randu.sgi.com
From: robert@randu.sgi.com (Robert Skinner)
Newsgroups: comp.graphics
Subject: Re: Bezier curves
Summary: Its Easy...
Message-ID: <41650@sgi.sgi.com>
Date: 12 Sep 89 21:40:00 GMT
References: <273@marvin.moncam.co.uk> <8358@spool.cs.wisc.edu>
Sender: robert@randu.sgi.com
Organization: Silicon Graphics, Inc., Mountain View, CA
Lines: 32

In article <8358@spool.cs.wisc.edu>, stuart@rennet.cs.wisc.edu (Stuart Friedberg) writes:
> kaush@moncam.co.uk (Kaush Kotak) writes:
> >Help! I need info on how to split a single (cubic) bezier curve into two. 
> >Given a t-value & 4 control points, how do I find values for the new control 
> >points?
> 
> There is probably a more direct method, but ....

	[ description deleted ]

There is a very simple way to do this from a construction you probably
already know.  To find a point at t=t0 along a Bezier with the
control points A, B, C, and D.  find the points t0 of the way from
A to B, B to C and C to D:  (You should draw a picture to follow along.)

	E = A + t0*(B - A)
	F = B + t0*(C - B)
	G = C + t0*(D - C)

repeat with the two segments you get:

	H = E + t0*(F - E)
	I = F + t0*(G - F)

and repeat again with the last segment:

	J = H + t0*(I - H)

You know J is on the curve, and it turns out that (A, E, H, J) and 
(J, I, G, D) are the control points for your two curves.

Robert