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From: thomas@utah-gr.UUCP
Newsgroups: net.graphics
Subject: Re: plotting on infinite domain
Message-ID: <1682@utah-gr.UUCP>
Date: Mon, 17-Feb-86 13:25:50 EST
Article-I.D.: utah-gr.1682
Posted: Mon Feb 17 13:25:50 1986
Date-Received: Wed, 19-Feb-86 01:04:21 EST
References: <325@watmps.UUCP>
Reply-To: thomas@utah-gr.UUCP (Spencer W. Thomas)
Distribution: net
Organization: University of Utah, Salt Lake City
Lines: 29

In article <325@watmps.UUCP> rhbartels@watmps.UUCP (Richard Bartels) writes:
>I want to be able to plot f(x) for x in the range [-infinity..infinity],
>likewise f(x) in [-infinity..infinity]  on a square screen.

You might think about a "stereographic" projection that maps the plane
onto a hemisphere (which you can then project straight down onto the
unit circle).  Here is a picture:

			     +      .      +
			     +       \     + unit hemisphere
			      +       \   +
				+      \+
plane:	---------------------------------------------------------------
	. is the center of the hemisphere,
	\ indicates a ray from there to the plane

The mapping of a point on the plane to the hemisphere is to project it
along a ray from the center of the hemisphere.  Algebraically, the point
(x,y) goes to the point (x/d, y/d, 1 - 1/d), where d is sqrt(1 + x^2 +y^2).
You can then discard the z coordinate (or not even compute it) to get a
mapping of the plane onto the circle.

If it is important to maintain the rectangular nature of the coordinate
plane (as it might be in plotting (x, f(x)), you could also apply the
projection in each coordinate independently, so that
	(x, f(x)) -> ( x / sqrt(1 + x^2), f(x) / sqrt(1 + f(x)^2) )

-- 
=Spencer   ({ihnp4,decvax}!utah-cs!thomas, thomas@utah-cs.ARPA)