Circles do not exist • Hacker News Board

Re: Circles do not exist

#11

Post by NegativeK » Tue, Sep 19, 2023, 8:14 PM UTC

> This is a laser cutter that takes its "print jobs" as a PDF file and uses its vector drawing commands to drive the cutting head. This means that it is impossible to use it to print a wheel. You'd need to attach the output to a lathe and sand it down to be round so it actually functions as a wheel rather than as a vibration source.

Respectfully, I don't think you're limited by the PDF format if you're talking about a laser cutter. And... Circular motion doesn't spring forth naturally from gantry CNC laser cutters -- they're rectilinear in design. It's circles not existing all the way down.

Using it as a CAD format with inherent fundamental shapes missing seems kind of funny, though.

Re: Circles do not exist

#12

Post by Animats » Tue, Sep 19, 2023, 8:15 PM UTC

PDF for CAD is silly. The problem is that laser cutters tend to take 2D vector image data as input, rather than G-Code like real CNC machines. You can definitely express a circular path in G-Code, and you expect a milling machine to cut one accurate to the precision of the mechanical parts of the machine. But laser cutter software is to some extent derived from printer technology. You can raster scan a picture onto a surface with a laser cutter.

Re: Circles do not exist

#13

Post by CharlesW » Tue, Sep 19, 2023, 8:17 PM UTC

fooofw wrote: post #5

wizofaus wrote: post #2

Doesn't PS have "arc"?

I was curious, so I looked up arc in the PostScript Language Reference [1]. It contains the following (p. 530): > The arc is represented internally by one or more cubic Bézier curves (see curveto) approximating the required shape. This is done with sufficient accuracy to produce a faithful rendition of the required arc. However, a program that reads the constructed path using pathforall will encounter curveto segment…

> The arc is represented internally by one or more cubic Bézier curves…

But that's a rendering implementation detail, no? Isn't the precision and accuracy of any digital or physical manifestation of a circle limited by implementation details and physics?

Re: Circles do not exist

#14

Post by jstanley » Tue, Sep 19, 2023, 8:19 PM UTC

hinkley wrote: post #9

For 3d printing. Lathes do circles all the time. But it would be difficult to rotate either the head or the bed around an arbitrary axis in order to print a proper circle.

The article has nothing to do with 3d printing.

Re: Circles do not exist

#15

Post by fooofw » Tue, Sep 19, 2023, 8:21 PM UTC

CharlesW wrote: post #13

fooofw wrote: post #5

Earlier quoted context omitted.

I was curious, so I looked up arc in the PostScript Language Reference [1]. It contains the following (p. 530): > The arc is represented internally by one or more cubic Bézier curves (see curveto) approximating the required shape. This is done with sufficient accuracy to produce a faithful rendition of the required arc. However, a program that reads the constructed path using pathforall will encounter curveto segment…

> The arc is represented internally by one or more cubic Bézier curves… But that's a rendering implementation detail, no? Isn't the precision and accuracy of any digital or physical manifestation of a circle limited by implementation details and physics?

Yes, I agree completely.

Re: Circles do not exist

#16

Post by andy_threos_io » Tue, Sep 19, 2023, 8:21 PM UTC

Real world manufacturing machines (CNCs) are using G codes. Like most laser cutters and engraves, Ex. LaserGrbl software for laser machines.

G codes in fact have command for arcs.

G02 establishes a mode for clockwise circular arcs. G03 establishes a mode for counter-clockwise circular arcs.

Re: Circles do not exist

#17

Post by mindslight » Tue, Sep 19, 2023, 8:21 PM UTC

> 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 are just abstractions to be approximated.

Re: Circles do not exist

#18

Post by tantalor » Tue, Sep 19, 2023, 8:22 PM UTC

  Time 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.

Re: Circles do not exist

#19

Post by BillinghamJ » Tue, Sep 19, 2023, 8:22 PM UTC

accrual wrote: post #4

That'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...

Re: Circles do not exist

#20

Post by neilk » Tue, Sep 19, 2023, 8:23 PM UTC

If 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/bezier-circle/

P.S. of course, a display intended for the human eye has much looser tolerances than a gear or wheel.