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Circles do not exist

nibblestew.blogspot.com

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Re: Circles do not exist

#191

Post by mlyle »

itishappy wrote: post #53
NegativeK wrote: post #11

> 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. Respectfully, I don't think you're limited by the PDF format if you're talking about…

Epilog claims (up to) 1200dpi resolution. Another comment mentioned the "standard bezier curve representation" is accurate to 0.03%. This means errors should start being observable with a circle as small as 3in. These are probably wildly optimistic assumptions, but it's still 10x smaller than the bed of their largest unit, and there's nothing to stop people from creating arcs of circles with radii even bigger than th…

The 1200DPI resolution is for engraving using rasterization, so, not really the same thing.

When you're cutting things on a laser, there's myriad sources of error. Odds are the optical path isn't completely square, so there's some cross coupling between axes. There's drive belts. The laser is often pulsed. There's taper.

Re: Circles do not exist

#192

Post by firebat45 »

shalmanese wrote: post #149
TheRealPomax wrote: post #60

Earlier quoted context omitted.

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 i…

>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.

Re: Circles do not exist

#193

Post by firebat45 »

delta_p_delta_x wrote: post #156
Kirby64 wrote: post #155

Earlier quoted context omitted.

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?

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

Don't try to logic how Americans measure things.

Re: Circles do not exist

#194

Post by armoredkitten »

ilove_banh_mi wrote: post #161
karaterobot wrote: post #90

> The only way to create a proper circle is to have a raster image like the one above. The raster image won't be a circle, it'll be a circle projected onto a square or rectangular grid. But, just like with the Bezier curves, nobody will notice. I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't both…

what if someone told you the painting's subject matter is not a Belgian pipe

Clarifying that the non-pipe is a Belgian non-pipe and not a French non-pipe reminds me of the joke with Sartre:

Jean-Paul Sartre was sitting in a cafe when a waitress approached him: "Can I get you something to drink, Monsieur Sartre?" Sartre replied, "Yes, I'd like a cup of coffee with sugar, but no cream". The waitress left, but returned a few minutes later and said, "I'm sorry, Monsieur Sartre, we are all out of cream -- how about with no milk?"

Re: Circles do not exist

#195

Post by delta_p_delta_x »

compiler-guy wrote: post #187
delta_p_delta_x wrote: post #156

Earlier quoted context omitted.

> 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?

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'...

Re: Circles do not exist

#196

Post by delta_p_delta_x »

edgineer wrote: post #184
delta_p_delta_x wrote: post #172

Earlier quoted context omitted.

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,…

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

File sizes too.

Re: Circles do not exist

#197

Post by TheRealPomax »

shalmanese wrote: post #149
TheRealPomax wrote: post #60

Earlier quoted context omitted.

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 i…

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.

Re: Circles do not exist

#198

Post by deaddodo »

mindslight wrote: post #128
deaddodo wrote: post #119

Earlier quoted context omitted.

The article is arguing mathematical inaccuracy, you're arguing the limitations of compressing an infinite abstract concept on a finite field. You're not wrong, but it's like someone showing proof that a person can't fly unassisted and then responding with "well dogs can't meow".

But the mathematical inaccuracy is caused by the limitations of compressing an abstract concept on a finite field (of a different base abstraction). So no, it doesn't seem like your wacky analogy at all.

No, the Bézier inaccuracy has nothing to do with rasterization. Did you even read the article?

They're saying that your arc for your circle will be incorrect before it's ever put into a concrete implementation. In other words, there's a base level inaccuracy and then your rasterization brings a whole new, different inaccuracy into play.

So yes, my "wacky analogy" is exactly apropos here.

Re: Circles do not exist

#199

Post by deaddodo »

Sharlin wrote: post #177
deaddodo wrote: post #117

Earlier quoted context omitted.

I could be completely incorrect here; but I don't know of a vector display that can do anything but arbitrary lines. Circles are usually rendered with sublinears to the command resolution (and trace runs) you're willing to sacrifice. An oscillating display can do curves, but only in a wave/ linear sequential fashion.

You're probably right, but I don't think there's any fundamental obstacle to controlling a CRT electron beam to trace arbitrary curves – there's vertical control and horizontal control and you can arbitrarily modulate them over time, can't you?

I didn't say it wasn't theoretically possible, I said there are no (that I know of) concrete implementations of this idea.

Yes, this is theoretically possible. I imagine it wasn't done due to processing limitations during the time vector displays were common; but my limited knowledge in the realm doesn't give me certainty.

Re: Circles do not exist

#200

Post by ElectricalUnion »

TeMPOraL wrote: post #171
karaterobot wrote: post #90

> The only way to create a proper circle is to have a raster image like the one above. The raster image won't be a circle, it'll be a circle projected onto a square or rectangular grid. But, just like with the Bezier curves, nobody will notice. I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't both…

> I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't bother measuring them to get the answer. I considered, and to this day consider, inaccurate figures in textbooks to be sloppy job by lazy people . Sure, measuring the solution off a drawing is (in math classes) missing the point of the exercise, b…

> inaccurate figures in textbooks

Sometimes it's not about being accurate, sometimes it's about the figures in the textbook representing unrepresentable, impossible situations on whatever geometry you're operating on. say euclidean geometry. Casual things like triangles where the sum of internal angles doesn't match π. Triangles where the sum of length of the two smaller sides is larger that the larger side.

Being able to reason about what are supposed to be the constraints of a otherwise impossible system is valuable in itself.

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