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Re: Circles
From: |
David Kastrup |
Subject: |
Re: Circles |
Date: |
Thu, 11 Aug 2022 14:14:10 +0200 |
User-agent: |
Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux) |
Werner LEMBERG <wl@gnu.org> writes:
>>> 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.
>
> This is not correct. PostScript-derived fonts (Type1, CFF/CFF2 in
> OpenType) *do* use third-order curves. I think you are mixing this up
> with TrueType fonts, which indeed use second-order curves.
I was more talking about the curveto operator than fonts, but you are
right either way. It was just Truetype that used only quadratic
Béziers.
Sort of embarrassing, since I distinctly remember putting explicit
quartercircle approximations into the curved rectangles PostScript code.
I did not find anything like that in the repository master though; it
must have been an ephemeral part of the work for better rasterized PDF
stems I did quite some time ago.
--
David Kastrup
- Circles, Andrew Bernard, 2022/08/10
Re: Circles, Andrew Bernard, 2022/08/11
Re: Circles, Andrew Bernard, 2022/08/11
Re: Circles, Silvain Dupertuis, 2022/08/11