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Circles do not exist

nibblestew.blogspot.com

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Re: Circles do not exist

#91
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.

Do you think there's a fundamental difference between how CNC, 3d printing, and laser cutting equipment behaves?

Re: Circles do not exist

#92

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.

This is true for almost every machine tool I've ever used (CNC mills, 3d printers, CNC plasma cutting, & water jet), but every laser cutter I've ever used (and I've used the kind that runs on 3-phase power and has no safety enclosure) speaks some variant of PCL. The one exception being a $300 home-brew tabletop laser running the aforementioned LaserGrbl...

That said, apart from a handful of misconfigurations, I've never had a problem getting any of them to cut out nice circles.

Re: Circles do not exist

#94

> 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…

Epilog claims (up to) 1200dpi resolution. Another comment mentioned the "standard bezier curve representation" is accurate to 0.03%. This means errors should start being observable with a circle as small as 3in. These are probably wildly optimistic assumptions, but it's still 10x smaller than the bed of their largest unit, and there's nothing to stop people from creating arcs of circles with radii even bigger than th…

Last time I used one, Epilog’s software was pretty terrible. It seemed to designed around a workflow in which you either design your cuts in CorelDraw and then print to a Windows print driver.

I sincerely hope that the upcoming Windows third-party print driver deprecation kills this.

(Also, what’s wrong with them? Even ignoring cost, I would rather have a Chinese printer that had a publicly known control interface and supported Lightburn than a “nice” American laser printer that was only operable with bad proprietary software.)

Re: Circles do not exist

#96
post #7

"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

If I put that through ps2pdf and remove compression, I can see:

  stream
  q 0.1 0 0 0.1 0 0 cm
  /R7 gs
  10 w
  0 G
  1500 1000 m
  1500 1276.14 1276.14 1500 1000 1500 c
  723.859 1500 500 1276.14 500 1000 c
  500 723.859 723.859 500 1000 500 c
  1276.14 500 1500 723.859 1500 1000 c 
  S
  Q
  endstream
i.e PDF has no arc command, it was converted to "c" bezier curves.

Re: Circles do not exist

#98
post #88
post #57

Earlier quoted context omitted.

If a Bézier-based circles with four nodes are too rough, I suppose a circle with 16 or 24 or 128 nodes can be made smooth enough to exceed the laser cutter's margin of error. If you want to produce a highly regular circle in Inkscape, draw a polygon with many nodes (say, 24), convert it to path, then make all nodes smooth and symmetric.

Or just use the ellipse (E) in Inkscape, set the start/end to 0, and hold down ctrl. Then inkscape will generate a ` ` svg element.

But the SVG in Inkscape is not a PDF on a machine that accepts PDF CAD drawings.

When you print to PDF, the circle will have to be approximated, which is what the article is talking about.

Re: Circles do not exist

#99
post #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.

Yeah, I don't know what effect he is talking about here. SVG has which I would assume is normally rasterized to pixel-level accuracy (as opposed to approximated with beziers), so there are lots of "perfect" circles to be found. https://developer.mozilla.org/en-US/docs/Web/SVG/Element/cir...

Re: Circles do not exist

#100

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…

I wouldn’t have believed you until I started looking into how spheres are made with various materials. All of them require immense amounts of iterations from rough cutting to polishing. Generally they are formed by reducing from a larger piece of material, sometimes inflated. It is never a cheap process to make a sphere and against nature is to achieve it. In the collection of gravities the earth and its inhabitants are subject to, straight lines are rare. A perfect sphere demands infinite straight lines of equal length from one point in space and for those to persist over time. A tall order for mere matter. Buckyballs are good enough for me.
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