10 ms·
Circles do not exist
- blue1 3y agoIs this true for Adobe Illustrator too (which has arc and ellipse tools)? Even if saved to .ai format?
- wizofaus 3y agoDoesn't PS have "arc"?
- fooofw 3y agoI 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 segments where arcs were specified originally. [1] https://www.adobe.com/jp/print/postscript/pdfs/PLRM.pdf https://www.adobe.com/jp/print/postscript/pdfs/PLRM.pdf
- CharlesW 3y ago> 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?
- proto_codex 3y agofact: circles are actually squares that have successfully deceived you. You have been bested by a shape.
- hinkley 3y agoSo you're saying you don't have to square a circle because it already is?
- thfuran 3y agoWell I have to say, that really freed up my weekend.
- retrocryptid 3y agoBut squares are really just diamonds which have been squished a bit.
- kevin_thibedeau 3y agoThey're all just superellipses.
- lo_zamoyski 3y agoA topologist once told me "square" and "circle" are synonyms.
- GuB-42 3y agoThat's a well known conspiracy theory that has been proven wrong long ago. You can't square the circle. Don't be so irrational.
- accrual 3y agoThat's pretty interesting. I'll now be doubting every circle I walk by, questioning if it's even real or just some approximation.
- BillinghamJ 3y agoPerfect shapes do not exist on a physical level, so they're all approximations https://factmyth.com/factoids/there-are-no-straight-lines-or-perfect-circles/ https://factmyth.com/factoids/there-are-no-straight-lines-or...
- nerdponx 3y agoCircles 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.
- kanzenryu2 3y agoThat's just a circular argument
- lo_zamoyski 3y agoA not-quite-circular argument, even!
- Puts 3y ago"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?
- CharlesW 3y ago> 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
- Puts 3y agoYes, but as someone else commented the arc is internally based on bézier curves. How accurate thee circle would be by plotting is probably dependent on the trigonometric table built in to the postscript interpreter, but at least it would be mathematically possible to make an accurate circle where it's actually not even possible to express a perfect circle with bézier curves.
- retrocryptid 3y agoIn theory you could, when you were converting from PS to G-Code NOT emulate the arc with bezier curves, but convert them into g-code circles. This would likely cause the laser cutter to cut something that looked SLIGHTLY different than the rendered PDF. But anyone who's worked in the field long enough knows that WYSIWYG is a lie (albeit a very useful lie.)
- Puts 3y agoDon't get me wrong. I'm not questioning the usefulness of béziers. I'm questioning the authors notion that postscript inherently is incapable of expressing accurate circles just because the language don't have built in primitives for them. :)
- 3y ago
- hinkley 3y agoFor 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.
- jstanley 3y agoThe article has nothing to do with 3d printing.
- deleted 3y ago[deleted]
- hinkley 3y agoDo you think there's a fundamental difference between how CNC, 3d printing, and laser cutting equipment behaves?
- c22 3y agoYes, several.
- hinkley 3y agoOkay, 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.
- c22 3y agoI 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.)
- NegativeK 3y ago> 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 a laser cutter. And... Circular motion doesn't spring forth naturally from gantry CNC laser cutters -- they're rectilinear in design. It's circles not existing all the way down. Using it as a CAD format with inherent fundamental shapes missing seems kind of funny, though.
- itishappy 3y agoEpilog 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 that!
- photonerd 3y agoObservable 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.
- Animats 3y agoPDF 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 surface with a laser cutter.
- mitthrowaway2 3y agoAgreed. 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.
- crote 3y agoDXF seems to be reasonably common for laser cutters. It at least supports arcs! I don't think many laser cutters use raster scanning, though. That's going to leave some really nasty artifacts. You really want to cut continuous lines like, well, lines.
- Animats 3y agoLaser engraving is usually raster scan, and most laser cutters can do both line cutting and raster scanning.
- tantalor 3y agoTime Cube's ineffable Truth. 'Cubeless Word' is not Truth. Word justifies all human evil. Time Cube is a test for Truth. Circle measure is slop bucket.
- Terr_ 3y agoTacking on another quote-for-amusement: > "This is why you're taking less field work? Because you're reading 'On Circles, Volume 12'?" > "I wrote it." > "Unsurprising." > "I have to rewrite it. All twelve volumes [...] our physics framework was completely wrong!" > "Even about, like, circles?" > Ikora turns to look Chalco in the eye. "Especially about circles." [0] https://www.ishtar-collective.net/entries/vesper-of-radius https://www.ishtar-collective.net/entries/vesper-of-radius
- andy_threos_io 3y agoReal 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.
- retrocryptid 3y agoI 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.
- c22 3y agoThis 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.
- mindslight 3y ago> 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 are just abstractions to be approximated.
- ars 3y agoYou 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.
- mindslight 3y agoI 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".
- ars 3y ago> 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. One approximates the circle to the limit of the chosen resultion, the other simply has an error. A small error, but an error nontheless.
- mindslight 3y agoNeither rectangular pixels nor Bezier curves are bases capable of perfectly/natively representing a circle. Either one can approximate a circle to within some arbitrarily chosen amount of error, based on increasing the number of pixels or the number of Bezier curve segments. For a given circle and DPI, one can figure out the minimum number of Bezier curves necessary to represent the circle such that rendering those Bezier curves out to pixels will get you the exact same result as having rendered the circle in pixels directly.
- neilk 3y agoIf you use the standard way to approximate a circle with Bezier curves, it will differ from a true circle by about 0.03%. The human eye is not capable of seeing the difference, and, as the OP mentioned, most people can't accurately eyeball a perfect circle anyway. This post shows the math behind that, and then shows that it could be made even better with a few different choices. https://spencermortensen.com/articles/bezier-circle/ https://spencermortensen.com/articles/bezier-circle/ P.S. of course, a display intended for the human eye has much looser tolerances than a gear or wheel.
- jprete 3y agoI think the OP is really just frustrated with the idea that CAD will use PDF and, in that application, 0.03% deviation can be too much.
- klysm 3y agoUsing a PDF where 0.03% matters is insane no?
- anamexis 3y agoYes, that's the point. 1. PDF is to become a standard CAD interchange format. 2. Using PDF where 0.03% matters is insane. 3. If CAD requires 0.03% tolerance, then using PDF as a standard CAD interchange format is insane. I would imagine you generally want arbitrary precision for CAD.
- Nevermark 3y agoAbsolutely! I cannot imagine a CAD system that can't symbolically represent what is actually desired. The model and its spec should be one and the same. Approximations also open the door to different precision versions. Not helpful when different parts from different sources need to be consistent. Models that approximate/vary from the ideal spec, created intentionally to match manufacturing limitations, are ok.
- b800h 3y agoThis 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.
- retrocryptid 3y agoI 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.
- goatlover 3y agoI thought his point was that the forms are memories of the divine because the material world does not provide such forms. You leave the cave when you stop being dominated by your senses and use your reason to apprehend universals.
- lo_zamoyski 3y agoI 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.
- NegativeLatency 3y agoEspecially if space is quantized
- Karellen 3y agoEven if space isn't quantized, matter is.
- deleted 3y ago[deleted]
- diogenes4 3y ago
- jackmott42 3y agoIf you play the game Quake 3 Arena, which was, I think, the first game to use bezier curves in 3d rendering, so that a column or arch could dynamically adjust how many polygons are used depending on view distance, the columns are visibly not round! Not something most people notice unless they are looking for it.
- retrocryptid 3y agoBut the OP mentioned it EXPLICITLY matters in his use case. Telling someone their use case doesn't matter is sort of a reddit thing to do.
- Sharlin 3y agoAnd these days GPUs have programmable tessellation shaders so they can semi-automatically make up more geometry as needed. I remember the Q3A Beziers were advertised as if the game rendered actual Beziers (which would in principle be possible in software but not on hardware… of the day, anyway), rather than just doing dynamic LoD approximation with your bog-standard triangles!
- mbfg 3y agocircles exist with NURBs, iirc. Now at some point you have to turn on individual pixels, so ....
- Sharlin 3y agoNot if you use a vector display!
- deaddodo 3y agoI 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.
- Sharlin 3y agoYou'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?
- deaddodo 3y agoI didn't say it wasn't theoretically possible, I said there are no (that I know of) concrete implementations of this idea. Yes, this is theoretically possible. I imagine it wasn't done due to processing limitations during the time vector displays were common; but my limited knowledge in the realm doesn't give me certainty.
- choonway 3y agobut until then, figuring out micron level tolerances over meters can be done with perfect circles using Non Uniform Rational B(Basis)-Splines.
- syspec 3y ago> 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.
- titzer 3y agoLook at a coffee cup.
- TeMPOraL 3y agoHow 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?
- InitialLastName 3y agoWith a coffee cup, you should be able to take a micrometer (or a piece of string) and verify roundness of the base object to whatever arbitrary precision your heart desires (and your reality will allow).
- TeMPOraL 3y agoI don't think I've ever seen a coffee cup that would let me do that. As I said earlier, I don't really trust their roundness, and that's on top of them usually being made of some kind of ceramic and thus having grain. (Maybe a cheap, single-use plastic cup would be smooth enough and stiff enough and round enough, given the production process.)
- ks2048 3y agoYeah, I don't know what effect he is talking about here. SVG has <circle> 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/circle https://developer.mozilla.org/en-US/docs/Web/SVG/Element/cir...
- edgarvaldes 3y agoI 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.
- rolph 3y agohttps://www.physicsforums.com/threads/the-planck-circle-problem.130303/ https://www.physicsforums.com/threads/the-planck-circle-prob...
- pfdietz 3y agoI was expecting this to be another "They have played us for absolute fools" meme.
- diogenes4 3y agoVery aggressive claim for solely talking about bezier representation.
- codexb 3y agoAs 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.
- bee_rider 3y agoUnfortunately PDF is, like, one of the most reassuring file formats. https://xkcd.com/1301/ https://xkcd.com/1301/ What would you put at the top? .PS is pretty fancy, although, just because it is probably saying “this is basically a PDF but from the olden days.”
- swores 3y agoThat comic is about what file types people choose to put what types of information (e.g. PDFs don't often get used for memes, and gifs don't often get used for scientific research papers). It's not even trying to make a point about the quality of the file formats themselves. (I assume when you wrote "most reassuring" you were instead interpreting it as a comic about the file types' ability to accurately hold the information a user wants them to hold, because "reassuring" as pertains to the comic's actual meaning would be completely irrelevant to this topic of whether or not PDF makes a good interchange format.)
- rustyminnow 3y agoYeah but that chart is saved as a PNG which is like, pretty low on the scale. I don't think we can trust anything on there.
- notatoad 3y agoi think that comic is from an earlier time when making PDFs was harder.
- dagw 3y agoPDF/A is the required format for delivering and archiving the final CAD drawings in many major civil engineering projects I've been involved in,
- 3y ago
- mcphage 3y agoThat laser cutter might take PDF files as input, but it certainly isn't the case with all laser cutters.
- c22 3y agoI 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.
- Sophistifunk 3y agoPlease note that most pistons and cylinder bores are also not circles ;-)
- userbinator 3y ago...and haven't been for at least 76 years: https://news.ycombinator.com/item?id=15397926 https://news.ycombinator.com/item?id=15397926 (Original page seems to have moved; it is now here: https://www.web.imperialclub.info/Repair/Lit/Master/003/index.htm https://www.web.imperialclub.info/Repair/Lit/Master/003/inde... )
- NotYourLawyer 3y ago>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. Just like how cows don’t look like cows on film![0] [0] https://www.youtube.com/watch?v=KbkNul4wQH0 https://www.youtube.com/watch?v=KbkNul4wQH0
- waffletower 3y agoI 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: https://ibb.co/P1KwLDm https://ibb.co/P1KwLDm
- pkulak 3y agoThat statement is just one of a million in the "calculus does not exist" realm, and is not nearly as interesting as this article was. EDIT: apologies for the tone; came off very snide on second read.
- waffletower 3y agoI don't think the statement attempted to invalidate the article, there are many gems inside, such as the idea that human perception elongates the vertical axis, etc.
- namru1620 3y agoYou wouldn't happen to have a link handy about that vertical axis perception thing would you, I l'm super curious about it.
- waffletower 3y agoI haven't been able to find anything corroborating the claim. But I, perhaps gullibly, shared the perception. Did find this somewhat related white paper during my short search: https://www.sciencedirect.com/science/article/pii/S0042698900000924 https://www.sciencedirect.com/science/article/pii/S004269890...
- A_D_E_P_T 3y agoThat'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 proton isn't perfectly spherical. Whether the electron and other subatomic particles are perfectly spherical cannot, as yet, be determined. (The electron seemingly has a diameter far below the Planck Length.) There are no very large circles or spheres, either. All astronomical bodies are somewhat flattened. So I dare say perfect circles and spheres do not really exist, save as idealized mathematical objects.
- carrozo 3y agoNot really related to the article but this reminded me of a beautiful quote I’ve had in my notes for many years: "To travel a circle is to journey over the same ground time and time again. To travel a circle wisely is to journey over the same ground as it is for the first time. In this way, the ordinary becomes extraordinary, and the circle, a path to where you wish to be. And when you notice at last that the path has circled back into itself, you realize that where you wish to be is where you have already been ... and always were."
- nick-of-time 3y agoI recommend anyone who finds this topic interesting watch the video The Continuity of Splines. It's a detailed discussion of how you derive Bèzier and higher-order curves to serve your purposes. https://www.youtube.com/watch?v=jvPPXbo87ds https://www.youtube.com/watch?v=jvPPXbo87ds
- TheRealPomax 3y agoBut did you know that one of the cases PDF is being considered (and, based on Internet rumors, is already being used) is as an interchange format for CAD drawings? Now it suddenly starts mattering. Not really? It's considered as an interchange format, not as the interchange format. If you have CAD/CAM work for parts that need precision machining measured in tenths or less, you're not using machines that accept PDF to begin with.
- johnnyworker 3y agoSorry for not just quoting the bit about the straight line not existing in nature, but I could not bring myself to reduce it all to just that. In 1952 I spoke of the civilization of make-believe, the one we must shake off, myself, the the first of all! I spoke of columns of gray men on the march toward sterility and self-destruction. The same year I used the term "transautomation" to show the way beyond the rationalism of technocrats toward a new creation in harmony with the laws of nature. In 1953 I realized that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without thought or feeling; it is a line which does not exist in nature. And that the line is the rotten foundation of our doomed civilization. Even if there are certain places where it is recognized that this line is rapidly leading to perdition, its course continues to be plotted. The straight line is the only sterile line, the only line which does not suit man as the image of God. The straight line is the forbidden fruit. The straight line is the curse of our civilization. Any design undertaken with the straight line will be stillborn. Today we are witnessing the triumph of rationalist knowhow and yet, at the same time, we find ourselves confronted with emptiness. An aesthetic void, desert of uniformity, criminal sterility, loss of creative power. Even creativity is prefabricated. We have become impotent. We are no longer able to create. That is our real illiteracy. - Friedensreich Hundertwasser, "Mouldiness Manifesto: Against rationalism in architecture" https://www.sfu.ca/~andrewf/MOULDINESS_MANIFESTO.htm https://www.sfu.ca/~andrewf/MOULDINESS_MANIFESTO.htm
- susam 3y agoThe first programming language I learnt to program in was Logo, namely IBM/LCSI PC Logo. It too did not have any command to draw curves or circles. However, we were taught to draw a "circle" using code like this: REPEAT 360 [FD 1 RT 1] But alas, circles did not exist! It is easy to realise that the above code does not attempt to draw a circle. These instructions specify a triacosiahexeacontagon instead. Screenshot: https://susam.net/blog/fd-100.html#circles https://susam.net/blog/fd-100.html#circles
- ks2048 3y agoArticle says “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.” Anyone have a reference for this?
- CBLT 3y agohttps://www.piotrlukaszkiewicz.pl/05_vertical-horizontal/?lang=en https://www.piotrlukaszkiewicz.pl/05_vertical-horizontal/?la... From reading this, the error with circles appears to be <1%. Also, obligatory mention whenever horizontal-vertical illusion comes up: https://www.nippon.com/en/japan-topics/c12403/ https://www.nippon.com/en/japan-topics/c12403/
- karaterobot 3y ago> 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 bother measuring them to get the answer. The circle represents a circle, it is not a circle. Wait til I tell you about this painting of a French pipe I saw one time.
- gerdesj 3y agoCeci n'est ... perhaps? There was a Greek bloke who had a thing about perfection and geometry. Eclad or something similar (OK: Euclid). At what point does the perfect approach reality or vice versa? The pipe in question might not be French - the painting was painted by a French person but you cannot imply the country of the pipe itself on that basis without additional evidence!
- bombcar 3y agoEuclid with diagrams is modernism! The original texts didn’t have them.
- ilove_banh_mi 3y agowhat if someone told you the painting's subject matter is not a Belgian pipe
- armoredkitten 3y agoClarifying that the non-pipe is a Belgian non-pipe and not a French non-pipe reminds me of the joke with Sartre: Jean-Paul Sartre was sitting in a cafe when a waitress approached him: "Can I get you something to drink, Monsieur Sartre?" Sartre replied, "Yes, I'd like a cup of coffee with sugar, but no cream". The waitress left, but returned a few minutes later and said, "I'm sorry, Monsieur Sartre, we are all out of cream -- how about with no milk?"
- 3y ago
- phyzome 3y agoNot really buying this. There are the other comments about how this is wrong, but also -- there's no side-by-side comparison!
- hwayne 3y agoAll the more reason to use SVGs! SVG has <circle> and <ellipse> elements.
- kevin_thibedeau 3y agoTechnically, you can procedurally rasterize a circle using a bitmap brush image from within Postscript.
- wrs 3y agoIronically, Bézier curves were invented for use in CAD. [0] [0] https://www.bricsys.com/en-us/blog/the-bezier-curve-how-car-design-influenced-cad https://www.bricsys.com/en-us/blog/the-bezier-curve-how-car-...
- thot_experiment 3y agoCorrect me if I'm wrong but PDF (and SVG for that matter) have a circle/arc primitives that can be translated G02/G03 commands when fed to a laser cutter/plotter/CNC?
- jmwilson 3y agoI ran into this when trying to make a vector version of the Smith chart [1] - which has a lot of circles. It turns out the inaccuracy from a 4-segment Bezier "circle" is significant when you need precisely intersecting arcs at the scale of a full letter/A4 page [2][3]. Ultimately, you can just increase the number of Bezier segments and make the error arbitrarily small; doubling to 8 segments was enough to eliminate the error on the chart even at extreme magnification. [1] https://www.penpapernomographic.com/pdf/smith-chart.pdf https://www.penpapernomographic.com/pdf/smith-chart.pdf [2] https://github.com/pgf-tikz/pgf/issues/817 https://github.com/pgf-tikz/pgf/issues/817 [3] https://camo.githubusercontent.com/0cc44db2e367356629d897c10e13318f049ecfa8f72d047ffc35c07f5371f569/68747470733a2f2f692e696d6775722e636f6d2f72694c527a6d7a2e706e67 https://camo.githubusercontent.com/0cc44db2e367356629d897c10...
- toss1 3y ago>>one of the cases PDF is being considered (and, based on Internet rumors, is already being used) is as an interchange format for CAD drawings? Now it suddenly starts mattering. If you have any component where getting a really accurate circle shape is vital (like pistons and their holes), suddenly all your components are slightly misshaped. Which would not be fun. Holy forking shirtballs - NO! The article rightly make a nice concise case against it. I'd add from my experience: perhaps PDF people think this would be a cool way to make more money, but only because they have not done any CAD/CAM/CNC work. Since I do CAD/CAM/CNC as a regular part of my work, and have spent time with PDF back to it's early days, that is a hard NOPE. But definitely a good nominee for the Bad Ideas Hall Of Fame, at least honorable mention. sheesh.
- deleted 3y ago[deleted]
- alanbernstein 3y agoIf your laser cutter only works with PDF files, switch to a setup that works with Lightburn.
- fanf2 3y agoI have a copy of the Postscript language reference manual from 1985, and it has an `arcto` operator for drawing proper circles. You can see it in the PLRM 3rd ed. on page 191 https://www.adobe.com/jp/print/postscript/pdfs/PLRM.pdf https://www.adobe.com/jp/print/postscript/pdfs/PLRM.pdf
- jskherman 3y agoOn a tangential note, TIL there's a field of mathematics called "digital topological groups": https://doi.org/10.1016/j.topol.2023.108644 https://doi.org/10.1016/j.topol.2023.108644
- remorses 3y ago== does not exist
- deleted 3y ago[deleted]
- somat 3y agoThe 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.
- butterisgood 3y agoI always figured one couldn’t verify a circle if they saw one because there is no way to compare anything to pi exactly. All we have is approximations right?