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: https://ibb.co/P1KwLDm
Circles do not exist
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Re: Circles do not exist
#62Earlier 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.
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.
Re: Circles do not exist
#63"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.
Re: Circles do not exist
#64I 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 statement is just one of a million in the "calculus does not exist" realm, and is not nearly as interesting as this article was.
EDIT: apologies for the tone; came off very snide on second read.
Re: Circles do not exist
#65 But did you know that one of the cases PDF is being considered (and, based on Internet rumors, is already being used) is as an interchange format for CAD drawings? Now it suddenly starts mattering.
Re: Circles do not exist
#66That's pretty interesting. I'll now be doubting every circle I walk by, questioning if it's even real or just some approximation.
Perfect shapes do not exist on a physical level, so they're all approximations https://factmyth.com/factoids/there-are-no-straight-lines-or...
What about black holes? Do non-rotating ones create perfect spheres?
Re: Circles do not exist
#67Not really related to the article but this reminded me of a beautiful quote I’ve had in my notes for many years:
"To travel a circle is to journey over the same ground time and time again. To travel a circle wisely is to journey over the same ground as it is for the first time. In this way, the ordinary becomes extraordinary, and the circle, a path to where you wish to be. And when you notice at last that the path has circled back into itself, you realize that where you wish to be is where you have already been ... and always were."
Re: Circles do not exist
#68I recommend anyone who finds this topic interesting watch the video The Continuity of Splines. It's a detailed discussion of how you derive Bèzier and higher-order curves to serve your purposes.
Re: Circles do not exist
#69As 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.”
Yeah but that chart is saved as a PNG which is like, pretty low on the scale. I don't think we can trust anything on there.
Re: Circles do not exist
#70This 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.
I think the point of Plato's endless yammering wasn't that they don't exist, but that you can't prove they exist and no one seems to have found one.
I thought his point was that the forms are memories of the divine because the material world does not provide such forms. You leave the cave when you stop being dominated by your senses and use your reason to apprehend universals.