Path: utzoo!mnetor!uunet!hsi!stevens
From: stevens@hsi.UUCP (Richard Stevens)
Newsgroups: comp.graphics
Subject: circles with non-unity aspect ratio
Message-ID: <807@hsi.UUCP>
Date: 5 Jan 88 01:31:15 GMT
Organization: Health Systems Intl., New Haven, CT
Lines: 38
Keywords: circle, aspect ratio, 3b1, ellipse

I am trying to draw "good" circles on an AT&T 3b1 (aka, UNIX PC).
The problem is the aspect ratio - it is nowhere near unity.
I have gone through McIlroy's paper ("Best Approximate Circles on
Integer Grids") and Foley & Van Dam.  I see two ways to draw the circle:

(1) Utilize "user coordinates" (in this case a 4096 by 4096 square)
	in which case I can use the algorithms as-is, however for each
	point on the 4096x4096 grid that I want to plot, I have to
	convert the point to device coordinates (430 by 288 for a
	square area on the 3b1).  However, I'd guess that this will
	lead to a "messy" circle (i.e., not meeting McIlroy's
	"thinness" or "connectivity" criteria).  Perhaps in this case,
	since I'd be going from a bigger coordinate space to a smaller
	one, there won't be any holes in the circle, but in general,
	I'd think a transformation like this could destroy some of
	the properties that the algorithm tries to preserve.
	Furthermore, this technique will take more time, since I'm
	calculating all the points on a 4096x4096 grid, when I'm really
	plotting on a much smaller area.  Each step of the loop will
	also require a transformation of the x and y coordinates,
	which will take more time.

(2) Utilize "device coordinates" (430 by 288, in this case).
	Here I need convert the circle parameters only once, instead
	of each time through the loop, however what I'm really drawing
	is an ellipse of pixels (that will appear as a circle on the
	screen).  The two references that I've looked at don't go into
	this case.

Am I missing something simple that would make it easy to draw my
circles ??  Can anyone point me to another reference that adequately
covers the drawing of a circle on a screen with a non-unity aspect
ratio (F & VD mention a few, but before I go digging up the articles,
does anyone know if these are what I should be looking at) ??

	Richard Stevens
	Health Systems International, New Haven, CT
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