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Subject: Re: [geda-user] libgeda circle parsing
From: John Doty <jpd AT noqsi DOT com>
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Date: Fri, 18 Jan 2013 08:50:43 -0700
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On Jan 18, 2013, at 7:13 AM, Markus Hitter wrote:

> 
> Am 18.01.2013 um 00:35 schrieb John Doty:
> 
>> Zero is a perfectly respectable radius for a circle to have. And as I've noted before, other objects of zero size can be handy.
> 
> I always thought you put emphasis on mathematically and logically correct models.

I do.

> In mathematics, there may be the special case of a circle with zero radius, but using this as a placeholder for something else is misuse.

I disagree. "A circle is the set of all points at a given distance from a given point." Thus, the mathematically and logically correct interpretation of a zero radius circle is the "given point", since it is at zero distance from itself, which no other point can be (let's not wander off into territory where old Berkeley would get upset, OK?).  There is no need for a separately encoded special case for points.

Different definitions, such as the usual parametric definition from analytic geometry, can even accommodate circles of negative radius. That can cause confusion for those who use the classical definition stated above. I'm therefore content to exclude negative radii.

> Plotting a zero-sized circle with a single display dot is misuse, too, and with the appearance of "retina" displays no longer useful either. Zero = zero = nothing.

By this reasoning, all lines should be invisible on the display also. They have zero width. But conventionally, in computer graphics, we widen them enough to be easily visible.

John Doty              Noqsi Aerospace, Ltd.
http://www.noqsi.com/
jpd AT noqsi DOT com