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Circles do not exist

nibblestew.blogspot.com

41–50 of 217 posts

Re: Circles do not exist

#41
post #22

This surprisingly less philosophical than I was expecting. There is no such thing as a perfect circle, it's a platonic ideal and lives in the Nous.

Depends on your definition of existence, i suppose, which greek ontology is notoriously bad at tackling.

Re: Circles do not exist

#42
post #25

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

Yes, but as someone else commented the arc is internally based on bézier curves. How accurate thee circle would be by plotting is probably dependent on the trigonometric table built in to the postscript interpreter, but at least it would be mathematically possible to make an accurate circle where it's actually not even possible to express a perfect circle with bézier curves.

In theory you could, when you were converting from PS to G-Code NOT emulate the arc with bezier curves, but convert them into g-code circles. This would likely cause the laser cutter to cut something that looked SLIGHTLY different than the rendered PDF. But anyone who's worked in the field long enough knows that WYSIWYG is a lie (albeit a very useful lie.)

Re: Circles do not exist

#44

If you play the game Quake 3 Arena, which was, I think, the first game to use bezier curves in 3d rendering, so that a column or arch could dynamically adjust how many polygons are used depending on view distance, the columns are visibly not round! Not something most people notice unless they are looking for it.

But the OP mentioned it EXPLICITLY matters in his use case. Telling someone their use case doesn't matter is sort of a reddit thing to do.

Re: Circles do not exist

#45
As someone who's spent a decent amount of time writing "output to pdf" routines, I would never in a million years choose pdf as an interchange format for anything at all.

Re: Circles do not exist

#46
post #30

> Furthermore, the human vision system is a bit weird and perfect circles look vertically elongated. You have to make them non-circular for people to consider them properly circular. Does any one have a link to a perfect circle, I'd love to see if it has the proposed effect on me.

Look at a coffee cup.

Re: Circles do not exist

#48
post #45

As someone who's spent a decent amount of time writing "output to pdf" routines, I would never in a million years choose pdf as an interchange format for anything at all.

Unfortunately PDF is, like, one of the most reassuring file formats.

https://xkcd.com/1301/

What would you put at the top?

.PS is pretty fancy, although, just because it is probably saying “this is basically a PDF but from the olden days.”

Re: Circles do not exist

#50
post #28

circles exist with NURBs, iirc. Now at some point you have to turn on individual pixels, so ....

but until then, figuring out micron level tolerances over meters can be done with perfect circles using Non Uniform Rational B(Basis)-Splines.
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