Circles do not exist

Post by ars » Wed, Sep 20, 2023, 1:45 AM UTC

mindslight wrote: post #127

ars wrote: post #78

Earlier quoted context omitted.

You completely missed his point. Pick a DPI, make a raster circle - it's accurate to the DPI you pick. Now use a Bezier to make that circle (and rasterize it to that DPI). It's not accurate to that DPI.

I don't see the conceptual difference between approximating a circle as a set of raster points, and approximating a circle as a Bezier curve. Also, it was the author's choice to frame the article in edgy universal terms "Circles do not exist" rather than something like a more pedestrian "Circles don't exist in PDF".

Post by thehappypm » Wed, Sep 20, 2023, 2:24 AM UTC

A_D_E_P_T wrote: post #86

waffletower wrote: post #61

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…

That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular. Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the pro…

Post by defrost » Wed, Sep 20, 2023, 2:50 AM UTC

thehappypm wrote: post #143

A_D_E_P_T wrote: post #86

Earlier quoted context omitted.

That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular. Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the pro…

What about orbits?

Post by waffletower » Wed, Sep 20, 2023, 2:57 AM UTC

namru1620 wrote: post #84

waffletower wrote: post #71

Earlier quoted context omitted.

I don't think the statement attempted to invalidate the article, there are many gems inside, such as the idea that human perception elongates the vertical axis, etc.

You wouldn't happen to have a link handy about that vertical axis perception thing would you, I l'm super curious about it.

Post by shalmanese » Wed, Sep 20, 2023, 3:47 AM UTC

TheRealPomax wrote: post #60

jprete wrote: 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.