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Circles do not exist

nibblestew.blogspot.com

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Re: Circles do not exist

#151

Post by laserbeam »

maxerickson wrote: post #134
jprete wrote: post #27

Earlier quoted context omitted.

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.

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.

Re: Circles do not exist

#152

Post by delta_p_delta_x »

TheRealPomax wrote: post #60
jprete wrote: post #27

Earlier quoted context omitted.

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.

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.

> 1/10th of a thou

What is this unit?

Re: Circles do not exist

#153

Post by [deleted] »

reilly3000 wrote: post #100
A_D_E_P_T wrote: post #86

Earlier quoted context omitted.

That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular. Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the pro…

I wouldn’t have believed you until I started looking into how spheres are made with various materials. All of them require immense amounts of iterations from rough cutting to polishing. Generally they are formed by reducing from a larger piece of material, sometimes inflated. It is never a cheap process to make a sphere and against nature is to achieve it. In the collection of gravities the earth and its inhabitants…

[deleted]

Re: Circles do not exist

#154

Post by Jerrrry »

A_D_E_P_T wrote: post #86
waffletower wrote: post #61

I thought the article would go further and posit that Circles do not exist in reality as they are approximations of a mathematical ideal. But the author does present the raster image as a bonafide circle, rather than the approximation that it truly is -- more resolved than others or not. A zoomed in excerpt of the author's rasterized circle approximation clearly shows that scale is key in perception of reified ideals…

That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular. Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the pro…

Large black holes are the most spherical things in the relative sense, not in an absolute sense; although more so than pico-black holes, which are not very spherical.

Light cones/the 4d-radii of causality are* perfectly spherical.

Re: Circles do not exist

#155

Post by Kirby64 »

delta_p_delta_x wrote: post #152
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.

> 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.

Re: Circles do not exist

#156

Post by delta_p_delta_x »

Kirby64 wrote: post #155
delta_p_delta_x wrote: post #152

Earlier quoted context omitted.

> 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?

Re: Circles do not exist

#158

Post by kbelder »

Jerrrry wrote: post #154
A_D_E_P_T wrote: post #86

Earlier quoted context omitted.

That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular. Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the pro…

Large black holes are the most spherical things in the relative sense, not in an absolute sense; although more so than pico-black holes, which are not very spherical. Light cones/the 4d-radii of causality are* perfectly spherical.

Aren't they warped by the curvature of space/time that they are spreading over?

Re: Circles do not exist

#159

Post by mrb »

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…

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.

Re: Circles do not exist

#160

Post by jstanley »

hinkley wrote: post #91
jstanley wrote: post #14

Earlier quoted context omitted.

The article has nothing to do with 3d printing.

Do you think there's a fundamental difference between how CNC, 3d printing, and laser cutting equipment behaves?

CNC and 3d printing typically use G-code, which has dedicated arc commands (G2, G3), and the laser cutter in the article uses PDF, which (apparently) does not, and is the main point of the article.

Of course any physical machine is only making an approximation of a circle (even a lathe doesn't turn perfectly round, there is no such thing), but at least for CNC and 3d printing you can specify a perfect circle. In PDF you can't.

(Yes, it is also true that a typical 3d print comes from an STL file, which can only specify triangles, so STL files also can only specify approximations of circles. But it is still true that most 3d printers run G-code, not PDF.)

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