8 ms·

if being off by 3 units on a 10,000 unit circle actually matters, you have stricter requirements than most industry bodies. If you're fabricating parts that hav

if being off by 3 units on a 10,000 unit circle actually matters, you have stricter requirements than most industry bodies. If you're fabricating parts that have tolerances measured in 1/10th of a thou, the machines you use absolutely don't ask for PDF, they ingest proper control code.

phkahler 3y ago
Control code generated from a CAD model, not a .pdf. Al you need to fix this is use rational Beziers - same thing but with weighted control points. STEP files will remain the standard for CAD.
- akira2501 3y ago
  > Al you need to fix this is use rational Beziers - same thing but with weighted control points. Then it is settled, we'll use .TTF as our CAD interchange format.
- jrockway 3y ago
  Does STEP not have circles? Because g-code has G2 which seems like it should draw an actual circle (G2 X0 Y0 R100 or similar).
  - yetihehe 3y ago
    STEP has circles and arcs. It's only PDF that's missing them.
shalmanese 3y ago
It absolutely matters. The type of fit you get between a shaft and a hole differs on the order of 5 - 10 microns [1]. A micron is 0.01% of a cm so 0.03% can consume a large portion of your tolerance budget. For example, you can make a shaft that fits in a hole like a spring because it can slide freely but air can't get out and you can shave a few microns off and it will sink into the hole at a controlled rate. This is all easily achievable in a home machine shop on a manual lathe. With Wire EDM, you can achieve even tighter tolerances and it would be perfectly possible to generate a part that could fit but could not spin because of the PDF error. [1] https://en.wikipedia.org/wiki/Interference_fit https://en.wikipedia.org/wiki/Interference_fit
- mrb 3y ago
  It doesn't matter. The error is 0.03% only with one of the most simplistic approximations of 1 Bézier curve per quarter circle. Bump this to 2 or 4 curves, and the error drops to 4.0e-6 or 6.2e-8 (https://pomax.github.io/bezierinfo/#circles_cubic https://pomax.github.io/bezierinfo/#circles_cubic) You are going to have a really hard time finding an industrial application where a 6.2e-8 error matters. In fact, check this out: the Epilog Fusion M2 40 laser machine that the author chooses to picture as the problem instance can engrave a circle of at most 28-inch diameter, and has a resolution of 1200 dpi. Therefore two (gasp!) Bézier curves per quarter circle offers far more precision (4.0e-6) than this machine's error (1/1200/28 = 3.0e-5). Edit: or take the world's roundest object: a sphere made out of a single crystal of silicon-28 atoms, with a roundness delta of less than 50 nanometres over a 93.6 mm diameter (https://www.heason.com/news-media/technical-blog-archive/world-s-roundest-object https://www.heason.com/news-media/technical-blog-archive/wor...) This is an error of 5.3e-7. Four puny Bézier curves per quarter circle (6.2e-8) are more perfect than this sphere.
  - shalmanese 3y ago
    That's the answer to a different question. I was just pointing out that, in most industrial applications, 0.03% tolerances are rarely seen but in the specific question of circular dimensions, it's a pretty common requirement. And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application.
    - mlyle 3y ago
      When we're talking about a CO2 laser, the errors from taper, variations in laser power, rigidity, trueness of optical path, etc, etc, far exceed 0.03%. If you want a circle that's better than a 0.03% tolerance, odds are you're not making it by tracing a circular path in g-code, but instead using something like a lathe. > And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application. A lot of work on CO2 lasers you do with something like Coreldraw or Inkscape. You absolutely can pick the number of vertices with some slight work. Lasers are a bit weird in that most of their work is for signmaking. Most end-user use cases are closer to a printer than that of a typical CNC machine. Indeed, it can be annoying to take something from CAD to lasers that want PDF, because you can end up with things like the resultant PDF not joining lines together properly into one shape and the laser "stopping" on each vertex. You end up pretty carefully picking tools and processes for this flow. Ideally you figure out how to give the laser a dxf...
delta_p_delta_x 3y ago
> 1/10th of a thou What is this unit?
- Kirby64 3y ago
  The standard industry term for a thousandth of an inch. Also called a mil. https://en.m.wikipedia.org/wiki/Thousandth_of_an_inch https://en.m.wikipedia.org/wiki/Thousandth_of_an_inch A 1/10th of a thou is 1/10000th of an inch, or 2.54 micrometers. It's insanely small.
  - delta_p_delta_x 3y ago
    > a thousandth of an inch. Also called a mil Why, America... At that point, if it's inventing new units to decimalise USC units, why not just use micrometres?
    - hanche 3y ago
      Or they could stick with binary and introduce a name for 1/1024th of an inch. Borrow a meme from the “almost SI” prefixes kibi, mebi, gibi etc., and call it a mibi, perhaps? ;-)
      - flangola7 3y ago
        What the hell are kibi and gibi?
        hanche 3y ago
        Kibibyte: 1024 bytes. Gibibyte: 2^30 or 1,073,741,824 bytes. The -bi suffix is intended to signify “binary”.
        delta_p_delta_x 3y ago
        They are IEC prefixes, complementary to the SI prefixes, and they only are defined for positive exponents. kibi : ki : 2^10 mebi : Mi : 2^20 gibi : Gi : 2^30 tebi : Ti : 2^40 ... Conveniently, these numbers are fairly close to 10^3, 10^6, 10^9, and 10^12 respectively (but with increasing error: 2^40 is almost 10% larger than 10^12, whereas 2^10 is only 2.4% larger than 10^3). This leads to a lot of conflation, mess, and misreporting by vendors and OS authors. Windows is an egregious example. A 1 TB (terabyte, 10^12) disk is reported in Windows as 931.7 GB. It ought to be 931.7 GiB, which is what Linux does. macOS uses the correct number but SI prefixes, so 1 TB is reported as 1 TB.

phkahler 3y ago

Control code generated from a CAD model, not a .pdf. Al you need to fix this is use rational Beziers - same thing but with weighted control points. STEP files will remain the standard for CAD.

akira2501 3y ago
> Al you need to fix this is use rational Beziers - same thing but with weighted control points. Then it is settled, we'll use .TTF as our CAD interchange format.
jrockway 3y ago
Does STEP not have circles? Because g-code has G2 which seems like it should draw an actual circle (G2 X0 Y0 R100 or similar).
- yetihehe 3y ago
  STEP has circles and arcs. It's only PDF that's missing them.

shalmanese 3y ago

It absolutely matters. The type of fit you get between a shaft and a hole differs on the order of 5 - 10 microns [1]. A micron is 0.01% of a cm so 0.03% can consume a large portion of your tolerance budget. For example, you can make a shaft that fits in a hole like a spring because it can slide freely but air can't get out and you can shave a few microns off and it will sink into the hole at a controlled rate. This is all easily achievable in a home machine shop on a manual lathe. With Wire EDM, you can achieve even tighter tolerances and it would be perfectly possible to generate a part that could fit but could not spin because of the PDF error. [1] https://en.wikipedia.org/wiki/Interference_fit https://en.wikipedia.org/wiki/Interference_fit

mrb 3y ago
It doesn't matter. The error is 0.03% only with one of the most simplistic approximations of 1 Bézier curve per quarter circle. Bump this to 2 or 4 curves, and the error drops to 4.0e-6 or 6.2e-8 (https://pomax.github.io/bezierinfo/#circles_cubic https://pomax.github.io/bezierinfo/#circles_cubic) You are going to have a really hard time finding an industrial application where a 6.2e-8 error matters. In fact, check this out: the Epilog Fusion M2 40 laser machine that the author chooses to picture as the problem instance can engrave a circle of at most 28-inch diameter, and has a resolution of 1200 dpi. Therefore two (gasp!) Bézier curves per quarter circle offers far more precision (4.0e-6) than this machine's error (1/1200/28 = 3.0e-5). Edit: or take the world's roundest object: a sphere made out of a single crystal of silicon-28 atoms, with a roundness delta of less than 50 nanometres over a 93.6 mm diameter (https://www.heason.com/news-media/technical-blog-archive/world-s-roundest-object https://www.heason.com/news-media/technical-blog-archive/wor...) This is an error of 5.3e-7. Four puny Bézier curves per quarter circle (6.2e-8) are more perfect than this sphere.
- shalmanese 3y ago
  That's the answer to a different question. I was just pointing out that, in most industrial applications, 0.03% tolerances are rarely seen but in the specific question of circular dimensions, it's a pretty common requirement. And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application.
  - mlyle 3y ago
    When we're talking about a CO2 laser, the errors from taper, variations in laser power, rigidity, trueness of optical path, etc, etc, far exceed 0.03%. If you want a circle that's better than a 0.03% tolerance, odds are you're not making it by tracing a circular path in g-code, but instead using something like a lathe. > And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application. A lot of work on CO2 lasers you do with something like Coreldraw or Inkscape. You absolutely can pick the number of vertices with some slight work. Lasers are a bit weird in that most of their work is for signmaking. Most end-user use cases are closer to a printer than that of a typical CNC machine. Indeed, it can be annoying to take something from CAD to lasers that want PDF, because you can end up with things like the resultant PDF not joining lines together properly into one shape and the laser "stopping" on each vertex. You end up pretty carefully picking tools and processes for this flow. Ideally you figure out how to give the laser a dxf...

delta_p_delta_x 3y ago

> 1/10th of a thou What is this unit?

Kirby64 3y ago
The standard industry term for a thousandth of an inch. Also called a mil. https://en.m.wikipedia.org/wiki/Thousandth_of_an_inch https://en.m.wikipedia.org/wiki/Thousandth_of_an_inch A 1/10th of a thou is 1/10000th of an inch, or 2.54 micrometers. It's insanely small.
- delta_p_delta_x 3y ago
  > a thousandth of an inch. Also called a mil Why, America... At that point, if it's inventing new units to decimalise USC units, why not just use micrometres?
  - hanche 3y ago
    Or they could stick with binary and introduce a name for 1/1024th of an inch. Borrow a meme from the “almost SI” prefixes kibi, mebi, gibi etc., and call it a mibi, perhaps? ;-)
    - flangola7 3y ago
      What the hell are kibi and gibi?
      - hanche 3y ago
        Kibibyte: 1024 bytes. Gibibyte: 2^30 or 1,073,741,824 bytes. The -bi suffix is intended to signify “binary”.
      - delta_p_delta_x 3y ago
        They are IEC prefixes, complementary to the SI prefixes, and they only are defined for positive exponents. kibi : ki : 2^10 mebi : Mi : 2^20 gibi : Gi : 2^30 tebi : Ti : 2^40 ... Conveniently, these numbers are fairly close to 10^3, 10^6, 10^9, and 10^12 respectively (but with increasing error: 2^40 is almost 10% larger than 10^12, whereas 2^10 is only 2.4% larger than 10^3). This leads to a lot of conflation, mess, and misreporting by vendors and OS authors. Windows is an egregious example. A 1 TB (terabyte, 10^12) disk is reported in Windows as 931.7 GB. It ought to be 931.7 GiB, which is what Linux does. macOS uses the correct number but SI prefixes, so 1 TB is reported as 1 TB.