Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Circles do not exist

nibblestew.blogspot.com

Post reply on HN
Print view View original

31–40 of 217 posts

Re: Circles do not exist

#31

Post by Sharlin »

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, but as the article notes, there are applications where you need a circle way more precise than one approximated by just a few Bezier curves. Although you could argue that any finite precision can be achieved by simply using more Bezier curves.

Re: Circles do not exist

#32

Post by edgarvaldes »

I very like this kind of blog posts: simple, clear, to the point. I don't need to summarize it myself, I dont need to wonder if the preamble, history, anecdata, midjourney pics and diagrams are really necessary to understand the main topic.

Re: Circles do not exist

#34

Post by mitthrowaway2 »

Animats wrote: post #12

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…

Agreed. PDF for CAD has its place, but its place is shop drawings read by humans, not as a machine interchange format. Many laser cutters will accept other vector formats, like DXF, which do have precise representation for circles.

Re: Circles do not exist

#36

Post by retrocryptid »

b800h wrote: post #22

This 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.

Re: Circles do not exist

#37

Post by nerdponx »

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.

Circles also don't exist in the core geospatial data library GEOS. You have to approximate them with a polygon that has a lot of vertices.

Re: Circles do not exist

#39

Post by retrocryptid »

andy_threos_io wrote: post #16

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.

I think the OP's concern was that they couldn't upload G-Code, they could only upload PDFs. And because PDFs don't encode circles, a mechanistic translation to G-Code can't convert it into a G-Code circle, only a curve that emulates a circle.

So... you know... note to self... when designing a laser cutter, allow the user to upload G-Code.

Post reply on HN