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Circles do not exist

nibblestew.blogspot.com

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Re: Circles do not exist

#171

Post by TeMPOraL »

karaterobot wrote: post #90

> The only way to create a proper circle is to have a raster image like the one above. The raster image won't be a circle, it'll be a circle projected onto a square or rectangular grid. But, just like with the Bezier curves, nobody will notice. I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't both…

> I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't bother measuring them to get the answer.

I considered, and to this day consider, inaccurate figures in textbooks to be sloppy job by lazy people. Sure, measuring the solution off a drawing is (in math classes) missing the point of the exercise, but at the same time, humans process knowledge holistically, so inaccurate drawings will interfere with gaining an intuitive understanding of a problem space.

I mean, if you were using software to chart some data you want to "get a feel for", would you be fine with software introducing arbitrary errors just because "Ceci n'est pas une pipe" or whatever?

Re: Circles do not exist

#172

Post by delta_p_delta_x »

flangola7 wrote: post #166
hanche wrote: post #165

Earlier quoted context omitted.

Or they could stick with binary and introduce a name for 1/1024th of an inch. Borrow a meme from the “almost SI” prefixes kibi, mebi, gibi etc., and call it a mibi, perhaps? ;-)

What the hell are kibi and gibi?

They are IEC prefixes, complementary to the SI prefixes, and they only are defined for positive exponents.

  kibi : ki : 2^10
  mebi : Mi : 2^20
  gibi : Gi : 2^30
  tebi : Ti : 2^40
  ...
Conveniently, these numbers are fairly close to 10^3, 10^6, 10^9, and 10^12 respectively (but with increasing error: 2^40 is almost 10% larger than 10^12, whereas 2^10 is only 2.4% larger than 10^3).

This leads to a lot of conflation, mess, and misreporting by vendors and OS authors. Windows is an egregious example. A 1 TB (terabyte, 10^12) disk is reported in Windows as 931.7 GB. It ought to be 931.7 GiB, which is what Linux does. macOS uses the correct number but SI prefixes, so 1 TB is reported as 1 TB.

Re: Circles do not exist

#173

Post by TeMPOraL »

reilly3000 wrote: post #100
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…

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…

But isn't the nature of attractive forces, like gravity, to squish everything into perfect spheres? The matter wants to resist, but that's another topic. The main issue is that pesky rotation - angular momentum is a blemish on the otherwise perfect equations of the cosmos.

Re: Circles do not exist

#174

Post by TeMPOraL »

titzer wrote: post #46
syspec wrote: 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.

Look at a coffee cup.

How can I distinguish between errors of perception, errors in manufacturing, and errors of perception of the designer who eyeballed circles on a computer screen with non-square pixels?

Re: Circles do not exist

#175

Post by dagw »

codexb wrote: post #45

As someone who's spent a decent amount of time writing "output to pdf" routines, I would never in a million years choose pdf as an interchange format for anything at all.

PDF/A is the required format for delivering and archiving the final CAD drawings in many major civil engineering projects I've been involved in,

Re: Circles do not exist

#176

Post by [deleted] »

flangola7 wrote: post #166
hanche wrote: post #165

Earlier quoted context omitted.

Or they could stick with binary and introduce a name for 1/1024th of an inch. Borrow a meme from the “almost SI” prefixes kibi, mebi, gibi etc., and call it a mibi, perhaps? ;-)

What the hell are kibi and gibi?

[deleted]

Re: Circles do not exist

#177

Post by Sharlin »

deaddodo wrote: post #117
Sharlin wrote: post #29

Earlier quoted context omitted.

Not if you use a vector display!

I could be completely incorrect here; but I don't know of a vector display that can do anything but arbitrary lines. Circles are usually rendered with sublinears to the command resolution (and trace runs) you're willing to sacrifice. An oscillating display can do curves, but only in a wave/ linear sequential fashion.

You're probably right, but I don't think there's any fundamental obstacle to controlling a CRT electron beam to trace arbitrary curves – there's vertical control and horizontal control and you can arbitrarily modulate them over time, can't you?

Re: Circles do not exist

#178

Post by layer8 »

laserbeam wrote: post #151
maxerickson wrote: post #134

Earlier quoted context omitted.

Seems like the real actual data would just be embedded inside the pdf. Hopefully anyway.

I don't think you can represent arbitrary data in a pdf AND have pdf viewers actually render it. If the pdf format screws precision (and I'm not surprised it does, it screws paragraphs and often only contains metadata to reconstruct lines of text), it should not be used as a data interchange format. Pdf is for print and human eyeballs. It's brilliant for those 2 things and not much else.

> I don't think you can represent arbitrary data in a pdf AND have pdf viewers actually render it.

You can have both in parallel, and have the editing software regenerate the rendered form from the source data form when anything changes. It’s not completely uncommon to use PDFs as a data carrier that way.

Re: Circles do not exist

#179

Post by colanderman »

delta_p_delta_x wrote: post #156
Kirby64 wrote: post #155

Earlier quoted context omitted.

The standard industry term for a thousandth of an inch. Also called a mil. https://en.m.wikipedia.org/wiki/Thousandth_of_an_inch A 1/10th of a thou is 1/10000th of an inch, or 2.54 micrometers. It's insanely small.

> a thousandth of an inch. Also called a mil Why, America... At that point, if it's inventing new units to decimalise USC units, why not just use micrometres?

Electronics manufacturing uses both with about equal frequency, often without unit names attached, and it's confusing as all hell, at least as a hobbyist. E.g. a 0603 footprint can mean 0.6×0.3 mm or 60×30 mils.

https://eepower.com/resistor-guide/resistor-standards-and-co...

Re: Circles do not exist

#180

Post by madengr »

c22 wrote: post #123
hinkley wrote: post #106

Earlier quoted context omitted.

Okay, well, that was informative. And explains why my point doesn't hold because I said a wrong word that has little to do with the point. Thanks for your efforts.

I don't know what you were trying to imply and I have no dog in this fight. But there are definitely fundamental differences between additive vs subtractive technologies, 2-axis vs 3-axis or multi-axis machining, and more niche machine-controlled manufacturing technologies, as well as very real differences behind the driving algorithms of most 3d printers/CNC machines vs most commercial laser cutters. (3d printers an…

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