Ironically, Bézier curves were invented for use in CAD. [0]
[0] https://www.bricsys.com/en-us/blog/the-bezier-curve-how-car-...
Circles do not exist
111–120 of 217 posts
Re: Circles do not exist
#112Article says “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.” Anyone have a reference for this?
https://www.piotrlukaszkiewicz.pl/05_vertical-horizontal/?la...
From reading this, the error with circles appears to be Also, obligatory mention whenever horizontal-vertical illusion comes up: https://www.nippon.com/en/japan-topics/c12403/
Re: Circles do not exist
#113> 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!
Euclid with diagrams is modernism! The original texts didn’t have them.
Re: Circles do not exist
#114Earlier quoted context omitted.
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.
> Do have a reference for PDF supporting circular arcs?
No, I could've sworn PDFs supported arcs but I was wrong. :) So when rendering/converting PostScript to PDF, circles/360° arcs must be converted to béziers.
Re: Circles do not exist
#115Correct me if I'm wrong but PDF (and SVG for that matter) have a circle/arc primitives that can be translated G02/G03 commands when fed to a laser cutter/plotter/CNC?
Re: Circles do not exist
#116If you use the standard way to approximate a circle with Bezier curves, it will differ from a true circle by about 0.03%. The human eye is not capable of seeing the difference, and, as the OP mentioned, most people can't accurately eyeball a perfect circle anyway. This post shows the math behind that, and then shows that it could be made even better with a few different choices. https://spencermortensen.com/articles/…
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.
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Re: Circles do not exist
#117circles exist with NURBs, iirc. Now at some point you have to turn on individual pixels, so ....
Not if you use a vector display!
I could be completely incorrect here; but I don't know of a vector display that can do anything but arbitrary lines. Circles are usually rendered with sublinears to the command resolution (and trace runs) you're willing to sacrifice.
An oscillating display can do curves, but only in a wave/ linear sequential fashion.
Re: Circles do not exist
#118I ran into this when trying to make a vector version of the Smith chart [1] - which has a lot of circles. It turns out the inaccuracy from a 4-segment Bezier "circle" is significant when you need precisely intersecting arcs at the scale of a full letter/A4 page [2][3]. Ultimately, you can just increase the number of Bezier segments and make the error arbitrarily small; doubling to 8 segments was enough to eliminate the error on the chart even at extreme magnification.
[1] https://www.penpapernomographic.com/pdf/smith-chart.pdf
[2] https://github.com/pgf-tikz/pgf/issues/817
[3] https://camo.githubusercontent.com/0cc44db2e367356629d897c10...
Re: Circles do not exist
#119> The only way to create a proper circle is to have a raster image like the one above. facepalm . A raster image can't express a circle either - it's also just an approximation. Same thing with a printout, for that matter. Maybe you could claim some kind of radial plotter is a true circle, but even there we're talking about pigment being absorbed along individual paper fibers. In reality, all the mathematical shapes…
The article is arguing mathematical inaccuracy, you're arguing the limitations of compressing an infinite abstract concept on a finite field.
You're not wrong, but it's like someone showing proof that a person can't fly unassisted and then responding with "well dogs can't meow".
Re: Circles do not exist
#120If you use the standard way to approximate a circle with Bezier curves, it will differ from a true circle by about 0.03%. The human eye is not capable of seeing the difference, and, as the OP mentioned, most people can't accurately eyeball a perfect circle anyway. This post shows the math behind that, and then shows that it could be made even better with a few different choices. https://spencermortensen.com/articles/…
The first "better" approximation, while having a better "max distance" (0.019608% vs 0.027253%), has a _worse_ span between min and max (0.039216% vs 0.027253%), which probably matters for some applications.