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From: laser-lovers@uw-beaver
Newsgroups: fa.laser-lovers
Subject: Re: LaserWriter/PostScript in BYTE
Message-ID: <764@uw-beaver>
Date: Wed, 6-Feb-85 02:40:09 EST
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Posted: Wed Feb  6 02:40:09 1985
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From: Gloger.es@XEROX.ARPA

You ask for an explanation of "Bezier cubics."

A Bezier curve is a particular kind of mathematical spline curve.  A
Bezier curve of order n is defined as a particular parametric function
of a sequence of n+1 control points, the function involving power terms
up to n.  The curve so defined passes through the two endpoints and
"tends toward" the in-between points.

A cubic Bezier curve is one of order 3, defined by 4 control points, and
using terms up to cubes in its defining function.

Beziers have a relatively large number of the properties which it is
useful for mathematical spline curves to have, for purposes both of
interactive definition and efficient drawing out.  Cubic Beziers seem to
be particularly good in this regard.


For an excellent technical presentation of the subject, see "Principles
of Interactive Computer Graphics," by William Newman and Robert Sproull.
(Newman and Sproull both worked at Xerox PARC during the writing of this
book.  Sproull is also the principal author of Xerox's Interpress
printing language.)