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Circles do not exist
201–210 of 217 posts
Re: Circles do not exist
#202Re: Circles do not exist
#203As 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.
Right, I like to joke that pdf is where data goes to die. But management loves them, so we continue making them.
As clarification, once the data goes in to a pdf it is a pain to get out again for further processing. Not impossible, but the format is clearly designed to put shapes on paper. anything more and you have to fight for it.
Re: Circles do not exist
#204The fact that postscript(and by implication pdf) encodes circles via bezier curves is an implementation detail, "arc" is a primitive of the language, there is no reason your PS to g-code interpreter would not use circles for arcs.
On that note, circles are rare on machine tools as well, if it is not a lathe(or rotary table) it will have to approximate a circle via a set of linear movements. Nothing wrong with this, modern machine tools can generate very good circles, often better than the rotary table, due to the additional error introduced by having another axis.
Re: Circles do not exist
#205Earlier quoted context omitted.
But the mathematical inaccuracy is caused by the limitations of compressing an abstract concept on a finite field (of a different base abstraction). So no, it doesn't seem like your wacky analogy at all.
No, the Bézier inaccuracy has nothing to do with rasterization. Did you even read the article? They're saying that your arc for your circle will be incorrect before it's ever put into a concrete implementation. In other words, there's a base level inaccuracy and then your rasterization brings a whole new, different inaccuracy into play. So yes, my "wacky analogy" is exactly apropos here.
You seem to be asserting some categorical difference between Bezier curves and pixels, likely because most output devices work in terms of pixels. But they're actually both just drawing primitives, and neither one is capable of representing perfect circles.
> the Bézier inaccuracy has nothing to do with rasterization
Obviously, because rasterization refers to pixels and has nothing to do with Bezier curves. On the other hand, that inaccuracy has everything to do with Bezierization.
> there's a base level inaccuracy and then your rasterization brings a whole new, different inaccuracy into play.
Yes, stacking two inexact transformations will result in more inaccuracy than a single one.
Since you seem to be attached to your analogy - it's more like a person making the argument that humans can't fly unassisted, while showing a picture of a pig as an example of flying, and I'm pointing out that pigs can't fly either.
Re: Circles do not exist
#206Earlier quoted context omitted.
No, the Bézier inaccuracy has nothing to do with rasterization. Did you even read the article? They're saying that your arc for your circle will be incorrect before it's ever put into a concrete implementation. In other words, there's a base level inaccuracy and then your rasterization brings a whole new, different inaccuracy into play. So yes, my "wacky analogy" is exactly apropos here.
You seem to be asserting some categorical difference between Bezier curves and pixels, likely because most output devices work in terms of pixels. But they're actually both just drawing primitives, and neither one is capable of representing perfect circles. > the Bézier inaccuracy has nothing to do with rasterization Obviously, because rasterization refers to pixels and has nothing to do with Bezier curves. On the ot…
You can post as large a wall of text as you like, your point is inaccurate regardless.
Re: Circles do not exist
#207Earlier quoted context omitted.
You seem to be asserting some categorical difference between Bezier curves and pixels, likely because most output devices work in terms of pixels. But they're actually both just drawing primitives, and neither one is capable of representing perfect circles. > the Bézier inaccuracy has nothing to do with rasterization Obviously, because rasterization refers to pixels and has nothing to do with Bezier curves. On the ot…
You can post as large a wall of text as you like, your point is inaccurate regardless.
no, you
Re: Circles do not exist
#208Earlier 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…
Lead shot is typically spherical without any trimming from a larger piece. The traditional method is called a shot tower, and involves dropping molten lead so it forms small drops that cool as they fall, until they impact into a water bath. This works because drops of liquid are spherical below a certain size dependent on the material. The classic depiction of a rain drop is entirely false.
Re: Circles do not exist
#209> 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…
The shape is there. postscript(and I assume PDF) has an arc primitive. however it is rasterized(drawn) in the reference implementation using bezier curves.
Now the postscript to servo control program(g-code?) interpreter might use the same bezier curve approximation, but it might not. I think if it were a formal complaint they would have to positively assert that their machined circles are following an inferior profile rather than just assume they are.
g-code sort of sucks as a language. It is very primitive. I always thought it would be cool to have a postscript dialect that supported more than two axis to use as a low level language on computer driven machine tools.
Re: Circles do not exist
#210> 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, b…
Looking back as a grown-up, I'm sure the teacher just said this to head off anyone considering cheating by making them think it would be a waste of time. The illustrations did look pretty close to accurate to me.