https://nibblestew.blogspot.com/2023/09/circles-do-not-exist.html

Nibble Stew

A gathering of development thoughts of Jussi Pakkanen. Some of you
may know him as the creator of the Meson build system. jpakkane at
gmail dot com

Tuesday, September 19, 2023

Circles do not exist

Many logos, drawings and other graphical designs have the following
shape in it. What is this shape?

[circle]

If you thought: "Ah-ha! I'm smart and read the title of this blog
post so I know that this is most definitely not a circle."

Well it is. Specifically it is a raster image of a circle that I
created with the Gimp just for this use.

However almost every "circle" you can see in printed media (and most
purely digital ones) are not, in fact, circles. Why is this?

Since roughly the mid 80s all "high quality" print jobs have been
done either in PostScript or, nowadays almost exclusively, in PDF.
They use the same basic drawing model, which does not have a
primitive for circles (or circle arcs). The only primitives they have
are straight line segments, rectangles and Bezier curves. None of
these can be used to express a circle accurately. You can only do an
approximation of a circle but it is always slightly eccentric. The
only way to create a proper circle is to have a raster image like the
one above.

Does this matter in the real world?

For printing probably not. Almost nobody can tell the difference
between a real circle and one that has been approximated with a
Bezier curve with just four points. Furthermore, the human vision
system is a bit weird and perfect circles look vertically elongated.
You have to make them non-circular for people to consider them
properly circular.

But suppose you want to use one of these things:

[797]

This is a laser cutter that takes its "print jobs" as a PDF file and
uses its vector drawing commands to drive the cutting head. This
means that it is impossible to use it to print a wheel. You'd need to
attach the output to a lathe and sand it down to be round so it
actually functions as a wheel rather than as a vibration source.

Again one might ask whether this has any practical impact. For this
case, again, probably not. But did you know that one of the cases PDF
is being considered (and, based on Internet rumors, is already being
used) is as an interchange format for CAD drawings? Now it suddenly
starts mattering. If you have any component where getting a really
accurate circle shape is vital (like pistons and their holes),
suddenly all your components are slightly misshaped. Which would not
be fun.

Extra bonus information

Even though it is impossible to construct a path that is perfectly
circular, PDF does provide a way to draw a filled circle. Here is the
relevant snippet from the PDF 2.0 spec, subsection 8.5.3.2:

    If a subpath is degenerate (consists of a single-point closed
    path or of two or more points at the same coordinates), the S
    operator shall paint it only if round line caps have been
    specified, producing a filled circle centred at the single point.

Who is willing to put money on the line that every PDF rendering
implementation actually uses circles rather than doing the simple
thing of approximating it with Beziers?

Posted by Jussi at 3:57 PM #
Email ThisBlogThis!Share to TwitterShare to FacebookShare to
Pinterest

No comments:

Post a Comment

 

Older Post Home
Subscribe to: Post Comments (Atom)

About Me

Jussi

View my complete profile

Blog Archive

  * V  2023 (32)
      + V  September (3)
          o Circles do not exist
          o A logo for CapyPDF
          o CapyPDF 0.5 is out
      + >  August (1)
      + >  July (3)
      + >  June (4)
      + >  May (4)
      + >  April (4)
      + >  March (6)
      + >  February (5)
      + >  January (2)

  * >  2022 (34)
      + >  December (4)
      + >  November (3)
      + >  October (2)
      + >  September (4)
      + >  August (2)
      + >  July (3)
      + >  June (2)
      + >  May (2)
      + >  April (4)
      + >  February (5)
      + >  January (3)

  * >  2021 (29)
      + >  December (1)
      + >  November (1)
      + >  October (1)
      + >  September (2)
      + >  August (1)
      + >  July (5)
      + >  June (3)
      + >  May (5)
      + >  April (2)
      + >  March (4)
      + >  February (3)
      + >  January (1)

  * >  2020 (42)
      + >  December (1)
      + >  November (5)
      + >  October (5)
      + >  September (2)
      + >  August (4)
      + >  July (5)
      + >  June (2)
      + >  May (4)
      + >  April (3)
      + >  March (4)
      + >  February (5)
      + >  January (2)

  * >  2019 (27)
      + >  December (4)
      + >  November (3)
      + >  October (1)
      + >  September (2)
      + >  August (3)
      + >  July (2)
      + >  June (2)
      + >  May (3)
      + >  April (1)
      + >  February (6)

  * >  2018 (24)
      + >  November (4)
      + >  October (1)
      + >  September (1)
      + >  August (3)
      + >  July (3)
      + >  June (1)
      + >  April (3)
      + >  March (4)
      + >  February (4)

  * >  2017 (35)
      + >  December (4)
      + >  November (1)
      + >  September (1)
      + >  August (3)
      + >  July (3)
      + >  June (3)
      + >  May (5)
      + >  April (4)
      + >  March (3)
      + >  February (2)
      + >  January (6)

  * >  2016 (20)
      + >  December (4)
      + >  November (2)
      + >  October (1)
      + >  September (2)
      + >  August (1)
      + >  July (1)
      + >  June (2)
      + >  May (2)
      + >  April (4)
      + >  March (1)

  * >  2015 (19)
      + >  December (2)
      + >  November (3)
      + >  October (3)
      + >  September (2)
      + >  August (3)
      + >  July (5)
      + >  June (1)

 
Simple theme. Powered by Blogger.