fact: circles are actually squares that have successfully deceived you. You have been bested by a shape.
So you're saying you don't have to square a circle because it already is?
Well I have to say, that really freed up my weekend.
Circles do not exist
21–30 of 217 posts
Re: Circles do not exist
#22This 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.
Re: Circles do not exist
#23Time Cube's ineffable Truth. 'Cubeless Word' is not Truth. Word justifies all human evil. Time Cube is a test for Truth. Circle measure is slop bucket.
Tacking on another quote-for-amusement:
> "This is why you're taking less field work? Because you're reading 'On Circles, Volume 12'?"
> "I wrote it."
> "Unsurprising."
> "I have to rewrite it. All twelve volumes [...] our physics framework was completely wrong!"
> "Even about, like, circles?"
> Ikora turns to look Chalco in the eye. "Especially about circles."
[0] https://www.ishtar-collective.net/entries/vesper-of-radius
Re: Circles do not exist
#24If 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.
Re: Circles do not exist
#25"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?
> 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.
Re: Circles do not exist
#26"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?
Also, I'd wager that you could get something closer to a circle with a naive bezier implementation than with a naive raster implementation, as long as you were willing to spend as much resources on storing curve nodes as you would on raster data. I mean, it's not like a rastered circle would make a good wheel either considering that technically every line on it is orthogonal.
Re: Circles do not exist
#27If 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.
Re: Circles do not exist
#28circles exist with NURBs, iirc. Now at some point you have to turn on individual pixels, so ....
Re: Circles do not exist
#29circles exist with NURBs, iirc. Now at some point you have to turn on individual pixels, so ....
Not if you use a vector display!
Re: Circles do not exist
#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.