Please note that most pistons and cylinder bores are also not circles ;-)
Circles do not exist
121–130 of 217 posts
Re: Circles do not exist
#122Earlier quoted context omitted.
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…
Observable is pushing it. Technically observable, sure, but ~1dpi misplaced is… unlikely to be noticeable. Plus, if that level of accuracy is required simply adding more nodes improves accuracy exponentially. Not least, the “standard” approximation really should be updated in software, as modern 4-node approximations are down to 0.005%, almost an order of magnitude better.
> simply adding more nodes improves accuracy exponentially
According to another comment, it actually improves at O(n^6).
Re: Circles do not exist
#123Earlier quoted context omitted.
Yes, several.
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 and other CNC tools have a pedigree stretching back to the original g-code developed in the 50s whereas laser cutters/engravers descend from more modern laser and inkjet printing technologies developed in the late 70s and 80s.)
Re: Circles do not exist
#124This 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.
Depends on your definition of existence, i suppose, which greek ontology is notoriously bad at tackling.
Greek, yes (owning to their paganism, which had trouble dealing with existence; it is not possible to conceptualize existence), but we see very deep insights in the medieval period, most notably in Thomas Aquinas. In the 20th century, we saw a particular brand of Thomism called existential Thomism that emphasized and expounded on Thomas' understanding of existence to help better appreciate it.
But I am not certain that is your criticism, or that this applies here? Platonism posits a third realm of ideas, one which Aristotle denies and attacks (and which Plato acknowledged), instead locating universals in things and in the intellect that grasps them. However, you can restore a kind of realm of ideas by interpreting it as (the mind of) God. So, universals exist in all three cases, though the manner in which they exist varies (e.g., in things as concrete instantiations, vs. in the human intellect as concepts abstracted from the concrete).
Re: Circles do not exist
#125This 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.
I would suggest more respect for Plato, frankly.
But I don't think that is right. He argued that matter existed in a relation of participation in the forms, that making such things like shadows or approximations of ideas. Aristotle deployed the third man argument to attack this notion. Plato conceded his view was problematic.
Re: Circles do not exist
#126That laser cutter might take PDF files as input, but it certainly isn't the case with all laser cutters.
I doubt that laser takes PDF natively, but probably converts from PDF using a custom print driver on the controlling PC. It is extremely likely this driver can also digest other formats.
Re: Circles do not exist
#127> 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…
You completely missed his point. Pick a DPI, make a raster circle - it's accurate to the DPI you pick. Now use a Bezier to make that circle (and rasterize it to that DPI). It's not accurate to that DPI.
I don't see the conceptual difference between approximating a circle as a set of raster points, and approximating a circle as a Bezier curve. Also, it was the author's choice to frame the article in edgy universal terms "Circles do not exist" rather than something like a more pedestrian "Circles don't exist in PDF".
Re: Circles do not exist
#128> 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…
The article is arguing mathematical inaccuracy, you're arguing the limitations of compressing an infinite abstract concept on a finite field. You're not wrong, but it's like someone showing proof that a person can't fly unassisted and then responding with "well dogs can't meow".
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.
Re: Circles do not exist
#129This 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.
That we can conceive of mathematical ideals like perfect circles that are never actually realized or encountered in the concrete, physical world (even if it is the case that they are possible in principle, in practice we arguably never encounter such things) suggests something very interesting about the nature of the human intellect.
And, in fact, even if they did exist physically, the very fact that the concept or predicate of Circularity exists in the intellect (and this concept must be Circularity as such or else we could not speak of circular things) and applies to many things despite their diversity, also suggests something about the intellect, namely, that it is not physical, as the physical is always concrete, instantiated, singular, this-and-not-that, not ideal.