mckee@canisius.UUCP (Douglas Mckee) (09/13/89)
Just today I was discussing with a professor of mine about the use of hexagonal pixels. Someone that I had talked to at Siggraph this year was telling me about how "in France there are monitors which use hexagonal pixels", yet my prof still believes that if a hexagonal tessalation is used, it is most likely converted into rectangular pixels. Could anyone point me into the right direction on this subject? Douglas McKee @relay.cs.net:mckee@canisius.edu
myers@hpfcdj.HP.COM (Bob Myers) (09/14/89)
>Just today I was discussing with a professor of mine about the use of >hexagonal pixels. Someone that I had talked to at Siggraph this year >was telling me about how "in France there are monitors which use >hexagonal pixels", yet my prof still believes that if a hexagonal >tessalation is used, it is most likely converted into rectangular >pixels. Could anyone point me into the right direction on this >subject? As far as the *monitor* is concerned, "hexagonal pixel" (or rectangular, for that matter) is a meaningless phrase. All the monitor knows is that the beam(s) in the CRT was turned on for X amount of time, during this particular scan line. The rise/fall times of the video amplifier, plus the shape of the beam itself (ignoring other shape-distoring items like geometry correction magnets) determines the shape of the spot. The electron beam itself is most often viewed as having a Gaussian cross-section; the best you can do, then as far as actual pixel shape in concerned is a circular spot (which actually falls off from the center in Gaussian manner along both axes). In reality, the limits of rise and fall times tend to distort this slightly, which is why single-pixel-wide vertical lines tend to be dimmer than single horizontal lines, unless your display system is smart enough to "stretch" single pixels. Color CRTs complicate this issue by placing a shadow mask in the path of the beam; however, the beams themselves are still Gaussian, and there is NEVER a guarantee that a given pixel in the image lines up precisely with exactly one red/green/blue phosphor triad, even when you're running at the highest resolution permitted by the phosphor pitch. The shape of a single pixel as displayed on the screen looks more like a circular spot viewed through a screen door; it is definitely not a nice clean square or rectangle. There may, for all I know, be monitors which use a shadow mask with hexagonal holes, but this will not produce hexagonal pixels - it'll just "screen" them differently. Your conceptual model of the image would still be a rectangular array of dots. (Unless there's somebody out there designing a REALLY funky frame buffer! :-)) Bob Myers KC0EW HP Graphics Tech. Div.| Opinions expressed here are not Ft. Collins, Colorado | those of my employer or any other myers%hpfcla@hplabs.hp.com | sentient life-form on this planet.
mmm@cup.portal.com (Mark Robert Thorson) (09/15/89)
mckee@canisius.UUCP says: > Just today I was discussing with a professor of mine about the use of > hexagonal pixels. Someone that I had talked to at Siggraph this year > was telling me about how "in France there are monitors which use > hexagonal pixels", yet my prof still believes that if a hexagonal I heard that in France the floppy disks have a hole for the disk head which goes from the center to a corner, unlike the rest of the world who use disks with holes that go from the center to a side. Typical French incompatibility by design.
wuethri@unizh.UUCP (Charles Wuethrich) (09/15/89)
To: unizh!cernvax!mcsun!uunet!ginosko!usc!rutgers!tut.cis.ohio-state.edu!ucbvax!hplabs!hpfcso!hpfcdj!myers Subject: Re: Hexagonal Pixels Newsgroups: comp.graphics In-Reply-To: <17400010@hpfcdj.HP.COM> References: <2477@canisius.UUCP> Organization: University of Zurich, Dept. of Computer Science Cc: mckee@canisius.edu Bcc: myers%hpfcla@hplabs.hp.com In article <17400010@hpfcdj.HP.COM> myers@hpfcdj.UUCP writes: >>Just today I was discussing with a professor of mine about the use of >>hexagonal pixels. Someone that I had talked to at Siggraph this year >>was telling me about how "in France there are monitors which use >>hexagonal pixels", yet my prof still believes that if a hexagonal >>tessalation is used, it is most likely converted into rectangular >>pixels. Could anyone point me into the right direction on this >>subject? > >As far as the *monitor* is concerned, "hexagonal pixel" (or rectangular, for >that matter) is a meaningless phrase. All the monitor knows is that the >beam(s) in the CRT was turned on for X amount of time, during this particular >scan line. The rise/fall times of the video amplifier, plus the shape of the >beam itself (ignoring other shape-distoring items like geometry correction >magnets) determines the shape of the spot. The electron beam itself is most >often viewed as having a Gaussian cross-section; the best you can do, then >as far as actual pixel shape in concerned is a circular spot (which actually >falls off from the center in Gaussian manner along both axes). In reality, >the limits of rise and fall times tend to distort this slightly, which is why >single-pixel-wide vertical lines tend to be dimmer than single horizontal >lines, unless your display system is smart enough to "stretch" single pixels. The issue is right, but......... You are forgetting about LCD screen displays. There is the factual possibility of building a screen based on hexagonal pixels......... with hexagonal (really Hexagonal) pixels. On the other hand, even on a CRT with slight modifications you could build a screen with "circular" pixels, the centers of which lie as the centers of a set of hexagons, all adjacent to each other and all equal, which covers the plane. In this case the pixels are indeed circular but..... They lie on a hexagonal grid...... (very easy thing to achieve this one). >array of dots. (Unless there's somebody out there designing a REALLY funky >frame buffer! :-)) This is an interesting one though, I am working on this subject since 3 years and the buffer isn't too much complicated... you can still use Cartesian coordinates, though you'll need to choose them non-orthogonal. Drop me a note if you are interested........ > > >Bob Myers KC0EW HP Graphics Tech. Div.| Opinions expressed here are not > Ft. Collins, Colorado | those of my employer or any other >myers%hpfcla@hplabs.hp.com | sentient life-form on this planet. Charles Wuethrich, Dept. of Computer Sciences | wuethri@ifi.unizh.ch Univ. of Zurich, 8057 Zurich-Irchel, Switzerland | k114910@czhrzu1a.bitnet
forsythe@convex.com (Charles Forsythe) (09/16/89)
mmm@cup.portal.com (Mark Robert Thorson) writes: >mckee@canisius.UUCP says: >> Just today I was discussing with a professor of mine about the use of >> hexagonal pixels [in France]. >I heard that in France [stupid joke]. >Typical French incompatibility by design. Could you portal-scum keep this garbage in alt.flame? Back to hexagonal pixels: A lot of the anti-aliasing (and other sub-pixel) work I've seen treats the pixels as circles. This works OK, but often on high-contrast edges (particularly on "medium-res" devices) the approximation introduces artifacts that cause unecessary blurring. In many cases, implementing square (pixel-shaped) filters is too computationally intense to be considered. Circles have the blissful property that they look the same rotated and are symetrical along any axis. Since hexagonal pixels are so much closer to circles, these useful approximations could be used with better results. The resulting hex-grid could probably be converted to a rectangular grid using pixel-shaped filters easily and might generate an image with fewer artifacts. Sounds like a reasonable idea to me... -Charles "I grew up being told the Russians were the enemy, they grew up being told we were the enemy. We were both wrong -- it's the French." -Billy Crystal in Moscow forsythe@convex.com #### This has nothing to do with Convex Computer Corportation -- obviously ####
rick@hanauma.stanford.edu (Richard Ottolini) (09/16/89)
Hexagonal grids are important for differential equation and cellula automata grids because they are more isotropic than rectangular grids (less funny stuff at 45-degree angles). I wonder if people use them in graphics?
bdb@becker.UUCP (Bruce Becker) (09/16/89)
In article <5351@portia.Stanford.EDU> rick@hanauma.UUCP (Richard Ottolini) writes: |Hexagonal grids are important for differential equation and cellula automata |grids because they are more isotropic than rectangular grids (less funny |stuff at 45-degree angles). I wonder if people use them in graphics? There is a quite extensive discussion of hexagonal grids in "Digital Halftoning", by Robert Ulichney, MIT Press, 1987. "Fascinating Reading" - Quiver & Quill "Not to Be Missed!" - New Yock Times Cheers, -- \__/ Bruce Becker Toronto, Ont. w \@@/ Internet: bdb@becker.UUCP, bruce@gpu.utcs.toronto.edu `/~/-e BitNet: BECKER@HUMBER.BITNET _< \_ Happiness is a warm gnu, yes it is - R. M. Soulman
nad@cl.cam.ac.uk (Neil Dodgson) (09/19/89)
In article <5351@portia.Stanford.EDU> rick@hanauma.UUCP (Richard Ottolini) writes: >Hexagonal grids are important for differential equation and cellula automata >grids because they are more isotropic than rectangular grids (less funny >stuff at 45-degree angles). [...] Wouldn't a hexagonal grid still give you "funny stuff" at 30-degree angles? On the other hand 30 < 45, so overall the odd effects should be much reduced using hexagonal rather than rectangular. Also, a hexagonal grid is the best that you can get (if you want all the pixels to be the same shape and tile the plane) because of the crystallographic restriction. Neil ==== Disclaimer: these are my opinions and do not neccesarily reflect the opinions of Cambridge University, or of my College, or of any of the other 30 colleges. Datclaimer: on the other hand trying to get all 32 organisations of the U of C to agree on ANYTHING would be a major feat in itself - bureaucrazy rules, U.K.
shf@well.UUCP (Stuart H. Ferguson) (10/09/89)
+-- nad@cl.cam.ac.uk (Neil Dodgson) writes: | In article <5351@portia.Stanford.EDU> rick@hanauma.UUCP (Richard Ottolini) writes: | >Hexagonal grids are important for differential equation and cellula automata | >grids because they are more isotropic than rectangular grids (less funny | >stuff at 45-degree angles). [...] | Wouldn't a hexagonal grid still give you "funny stuff" at 30-degree angles? No. The reason some cell-automata simulations use hexagonal packing for their cell positions is that the distance between cell centers is the same for all the nearest neighbors. The perimeter distance shared between neighbors is also uniform. This is presumably the same reason the war- gamers use them for their tactical simulations. You get around this nonsense that a diagonal move is sqrt(2) longer than a horizontal or vertical move. -- Stuart Ferguson (shf@well.UUCP) Action by HAVOC (ferguson@metaphor.com)