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From: hbaker@netcom.com (Henry G. Baker)
Subject: Hypertext paper on Gaussian Integers in Graphics HW & SW
Message-ID: <hbakerD1M8Dz.5Kr@netcom.com>
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Date: Fri, 30 Dec 1994 08:46:47 GMT
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The paper "Complex Gaussian Integers for 'Gaussian Graphics", ACM
Sigplan Notices 28, 11 (Nov 1993), 22-27, is available online in WWW
hypertext browsing ('html') form at URL

ftp://ftp.netcom.com/pub/hb/hbaker/Gaussian.html

--

Abstract

Some recent computer languages incorporate rational numbers, complex
numbers, and rational complex numbers.  We extend these numeric
facilities to deal properly with <i>Gaussian integers</i>--i.e.,
complex numbers whose real and imaginary parts are both ordinary
(rational) integers.  In addition to their intrinsic mathematical
interest, such extensions also raise interesting questions regarding
polymorphism and multiple inheritance.<p>

Since Gaussian integers are the coordinates of discrete square pixels
in the complex plane, complex operations can be used to implement 2-D
graphics operations.  Many 2-D algorithms are more elegant in complex
number form--e.g., one can envision a 2-D spreadsheet for scientific
applications whose coordinates are Gaussian integers.

----

This paper also shows the proper extension of certain standard
functions -- e.g., floor, ceiling, truncate, round, gcd, lcm, evenp,
oddp, numerator, denominator -- to Gaussian integers and Gaussian
fractions.

The paper also discusses the use of Gaussian number theory in the
construction of graphics frame buffers.

(Please excuse some broken links.  I haven't had time to add
construction sound-effects to these pages, yet :-)

----
Henry Baker
Read (192.100.81.1) ftp.netcom.com:/pub/hb/hbaker/README for ftp-able papers.
WWW archive: ftp://ftp.netcom.com/pub/hb/hbaker/home.html
************* Note change of address ^^^        ^^^^
(It _is_ accessible, but Netcom is loaded; keep trying.)

