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Circles do not exist

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101–110 of 217 posts

Re: Circles do not exist

#102
post #96

Earlier quoted context omitted.

> Just because there are no primitives for a circle… Is a 360° arc not a circle? %!PS /newpath 100 100 50 0 360 arc stroke showpage

If I put that through ps2pdf and remove compression, I can see: stream q 0.1 0 0 0.1 0 0 cm /R7 gs 10 w 0 G 1500 1000 m 1500 1276.14 1276.14 1500 1000 1500 c 723.859 1500 500 1276.14 500 1000 c 500 723.859 723.859 500 1000 500 c 1276.14 500 1500 723.859 1500 1000 c S Q endstream i.e PDF has no arc command, it was converted to "c" bezier curves.

That appears to be a rendering/conversion artifact since PDF also supports 360° arcs. My question is, mathematically, is a 360° arc not a circle? (I understand that once a circle is rendered or physically manifested, it's an approximation.)

Re: Circles do not exist

#103
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.

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.

Re: Circles do not exist

#104
post #96

Earlier quoted context omitted.

If I put that through ps2pdf and remove compression, I can see: stream q 0.1 0 0 0.1 0 0 cm /R7 gs 10 w 0 G 1500 1000 m 1500 1276.14 1276.14 1500 1000 1500 c 723.859 1500 500 1276.14 500 1000 c 500 723.859 723.859 500 1000 500 c 1276.14 500 1500 723.859 1500 1000 c S Q endstream i.e PDF has no arc command, it was converted to "c" bezier curves.

That appears to be a rendering/conversion artifact since PDF also supports 360° arcs. My question is, mathematically, is a 360° arc not a circle? (I understand that once a circle is rendered or physically manifested, it's an approximation.)

Do have a reference for PDF supporting circular arcs? I'm looking at the PDF reference manual and do not see it under list of path construction operators.

Re: Circles do not exist

#106
post #97
post #91

Earlier quoted context omitted.

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

Yes, several.

Okay, well, that was informative. And explains why my point doesn't hold because I said a wrong word that has little to do with the point.

Thanks for your efforts.

Re: Circles do not exist

#107
post #7

"The only primitives they have are straight line segments, rectangles and Bézier curves. The only way to create a proper circle is to have a raster image like the one above." Is this really an accurate conclusion? Just because there are no primitives for a circle – postscript is still a programming language so you can also plot a proper circle with trigonometry?

I was under the impression that the postscript in a pdf isn't a programming language. It is pre-executed so that only drawing primitives remain. But I could be wrong.

Nowadays PDF has JavaScript so sky's the limit.

Re: Circles do not exist

#110

> 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…

Ceci n'est ... perhaps?

There was a Greek bloke who had a thing about perfection and geometry. Eclad or something similar (OK: Euclid).

At what point does the perfect approach reality or vice versa?

The pipe in question might not be French - the painting was painted by a French person but you cannot imply the country of the pipe itself on that basis without additional evidence!

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