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Re: Circles

From: David Kastrup
Subject: Re: Circles
Date: Thu, 11 Aug 2022 11:23:36 +0200
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux)

Werner LEMBERG <> writes:

>>> There's a lot of oldish webpages with complex Bezier curve
>>> constructions for circles.
>> Those must be approximate constructions. It is not mathematically
>> possible to construct a Bézier curve which is at the same time an
>> exact circle.
> Well, Metafont uses a third-order Bézier approximation to build up
> circles (from four quarter circles).  However, the Metafont book says
> that the difference to a real circle is less than 0.06%, which is thus
> imperceptible.
> The same holds for PostScript-based fonts.

PostScript uses second-order Béziers, so it makes little sense to cite
the mathematics of Metafont here.

David Kastrup

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