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From: ken@turtlevax.UUCP (Ken "Turk" Turkowski)
Newsgroups: net.graphics
Subject: Re: Possible way of anti-aliasing.
Message-ID: <1233@turtlevax.UUCP>
Date: Tue, 7-Oct-86 03:21:16 EDT
Article-I.D.: turtleva.1233
Posted: Tue Oct  7 03:21:16 1986
Date-Received: Wed, 8-Oct-86 06:39:55 EDT
References: <280@joevax.UUCP> <265@hoqam.UUCP> <7151@utzoo.UUCP>
Reply-To: turk@apple.UUCP (Ken "Turk" Turkowski)
Organization: Apple Computer, Inc.
Lines: 25

For an analytic derivation of antialiasing for lines or polygons
given radially-symmetric point-spread function (PSF), look at:

	Anti-Aliasing through the use of Coordinate Transformations
	Turkowski, Kenneth
	ACM Transactions on Graphics
	Vol. 1, No. 3, July 1982, pp. 214-234

This outlines the transformation of the radially symmetric point-spread
function into another function which is the result of convolving the
line or polygon edge with the PSF.  One simply calculates the distance
of a pixel center from the edge, and uses that as an index into a table
which contains the proper value to put into the frame store.

The distance of successive pixels near an edge can be computed incrementally
through a linear coordinate transformation:
	du = a dx + b dy
where (b, -a) is a unit vector pointing from one vertex to the other.
If dx is 0, then a unit change in y (dy=1) produces a change in distance
of a (du=a).  This is just a normalized Bresenham algorithm.
-- 
Ken Turkowski @ Apple Computer, Cupertino, CA
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