161–170 of 217 posts
> 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…
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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.
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).
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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.
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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…
It followed PostScript which was a programming language that was intended to be directly undertood and runnable by Postscript enabled printers.
Postscript could easily do the job here, it had "arc" drawing primitives that described circles (both full and partial).
The 'failure' of Postscript was that as a programming languge a bad .ps job could crash a printer and a 1,500 page .ps document had to be internally fully rendered just to print out page 73 only (potentially code on any 'page' could loop back or forward and generate image elements on any page).
As a not-quite PostScript simplified 'other' the PDF formal languaage spec only allows the drawing of lines and 'curves' and curves are explicitly 3rd order bezier splines.
See: Path Operators (Page 95)
Portable Document Format Reference Manual (230 pages)
https://opensource.adobe.com/dc-acrobat-sdk-docs/pdfstandard...
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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?
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> 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? ;-)
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…
According to what? We have nothing that can measure anything close to that. The standard model doesn't predict any radius on the electron, just defining it as point-like.
> Whether the electron and other subatomic particles are perfectly spherical cannot, as yet, be determined.
How can we ever determine something to be perfectly spherical? Any measurement comes with finite precision, and maybe the thing is actually not a sphere if we measured with more precision?
All measurements we have done on the electric dipole moment of the electron suggests that it could be zero. (The standard model predicts it to be non-zero, but very very very small.) This suggests that the charge distribution of the electron is spherical (or very very very close to).
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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 th…
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.
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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.
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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?