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Comment by jprete | Hacker News Reader

I think the OP is really just frustrated with the idea that CAD will use PDF and, in that application, 0.03% deviation can be too much.

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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.

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

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)

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/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.

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.

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...

>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.

I can tell from this statement that you do not have a home machine shop with a manual lathe. Home machine shops most certainly do ~not~ typically (or easily) achieve micron accuracy.

In the category "using your hammer to screw in a rivet", you don't machine a shaft with a laser-cutter. As you point out: you use a lathe.

For "circular" work that you do use a laser cutter for, 0.03% tolerances are below the variance you get from the cutter itself. Expecting higher precision from the cutter that is somehow "messed up" by the deviation from the standard Bezier approximation of a circle, when the machine you're using can't give you that precision is using that proverbial hammer.

Of course, if that's really all you have access to (first of all: what are you even doing? look into buying a second hand lathe, or have everyone pitch in so your hobby space can buy one, they'll set you back less than a thousand bucks) the laser cutting is step one, you're not done after cutting, and you know you're not done after cutting because you know laser cutters are not high-precision machining tools like lathes or mills. You cut slightly oversized, and then you clean up the part and machine it down to final dimensions until your micrometer says you're within tolerance.

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.

> 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.

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).

STEP has circles and arcs. It's only PDF that's missing them.

> 1/10th of a thou

What is this unit?

The standard industry term for a thousandth of an inch. Also called a mil.

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.

> 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?

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? ;-)

What the hell are kibi and gibi?

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.

I think it's hard to call it misreporting when they've been reporting it the same way since before the standard you'd rather they use existed.

Wait, does MacOS report file sizes in base 10 as well, or just disks?

File sizes too.

Kibibyte: 1024 bytes. Gibibyte: 2^30 or 1,073,741,824 bytes. The -bi suffix is intended to signify “binary”.

Electronics manufacturing uses both with about equal frequency, often without unit names attached, and it's confusing as all hell, at least as a hobbyist. E.g. a 0603 footprint can mean 0.6×0.3 mm or 60×30 mils.

https://eepower.com/resistor-guide/resistor-standards-and-co...

Because at the time of the invention and adoption of this term of this term in the late 1850s, the metric system didn’t have widespread adoption at all. The treaty of the meter wasn’t until 1875.

So the metric system and decimalization of the inch are roughly contemporaneous and “just use this othe, also brand new system” isn’t an obvious choice at that point.

Fair enough.

I think the real question is... Why is such a unit still being used? I was under the impression that any serious ultra-precise CAD and machining was done in milli, micro, and nanometres. I thought pretty much any serious science or engineering had been metricated...

But then again I shouldn't be surprised; Americans measure the volume of lakes in 'acre-feet'...

I mean, a "thousandth" of an inch is also a decimalised USC unit.

Don't try to logic how Americans measure things.

Using a PDF where 0.03% matters is insane no?

Yes, that's the point.

1. PDF is to become a standard CAD interchange format.

2. Using PDF where 0.03% matters is insane.

3. If CAD requires 0.03% tolerance, then using PDF as a standard CAD interchange format is insane.

I would imagine you generally want arbitrary precision for CAD.

Absolutely!

I cannot imagine a CAD system that can't symbolically represent what is actually desired. The model and its spec should be one and the same.

Approximations also open the door to different precision versions. Not helpful when different parts from different sources need to be consistent.

Models that approximate/vary from the ideal spec, created intentionally to match manufacturing limitations, are ok.

Drawings for parts should have tolerances called out. I did mechanical inspection for a manufacturer for several summers. Every dimension had a plus/minus value listed. Holes and screw threads had go/no-go gauges

But is PDF really the standard CAD format for communicating with machines?

For laser cutting, I prefer to use SVG, as it's easier to generate. I had not really thought about precision, but SVG can represent circles directly.

Using PDF as a standard (for anything) is insane. I mean it was nice before Adobe backpedaled and tried to milk it for everything and now the format is anything but portable.

But could the CAD use more than 4 control points to approximate the circle better?

Seems like the real actual data would just be embedded inside the pdf.

Hopefully anyway.

I don't think you can represent arbitrary data in a pdf AND have pdf viewers actually render it. If the pdf format screws precision (and I'm not surprised it does, it screws paragraphs and often only contains metadata to reconstruct lines of text), it should not be used as a data interchange format.

Pdf is for print and human eyeballs. It's brilliant for those 2 things and not much else.

If I was dead set on using pdf as an interchange format, I'd make the standard that the pdf content was a drawing of the data and then also embed a better representation of the data. So a well formed file can be previewed with any pdf reader, but no problems with data quality when you go to use it for something.

Of course the drawing could then be out of step with the data, but so what.

> I don't think you can represent arbitrary data in a pdf AND have pdf viewers actually render it.

You can have both in parallel, and have the editing software regenerate the rendered form from the source data form when anything changes. It’s not completely uncommon to use PDFs as a data carrier that way.

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