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> This portion of signal theory only applies to a world made entirely out of frequencies. That's not precisely true: discrete blocks or edges can be approximat

> This portion of signal theory only applies to a world made entirely out of frequencies. That's not precisely true: discrete blocks or edges can be approximated arbitrarily closely in Fourier frequency space -- you just need to admit higher-frequency components. 'Pixel-sized square' is properly an oxymoron if you view pixels purely as samples -- a 'true' square can only be represented by an infinitely dense set of pixel samples. But this is a feature, not a bug, because neither computer monitors, nor the human eye, can render nor see a 'true' square either, only successively better approximations to them.

Dylan16807 10y ago
> That's not precisely true: discrete blocks or edges can be approximated arbitrarily closely in Fourier frequency space -- you just need to admit higher-frequency components. You can approximate those shapes, but that's an approximation. It's not impossible to do the math that way, but there are stumbling blocks to dodge. Like weird artifacts when you low-pass. > 'Pixel-sized square' is properly an oxymoron if you view pixels purely as samples -- a 'true' square can only be represented by an infinitely dense set of pixel samples. It's a square equal in size to the square-grid pixel spacing. It's not wrong, it's just being non-pedantic. > But this is a feature, not a bug, because neither computer monitors, nor the human eye, can render nor see a 'true' square either, only successively better approximations to them. A monitor does not quite deliver perfect squares, but what it displays is a lot closer to a square than to this shape: https://upload.wikimedia.org/wikipedia/commons/f/f8/Gibbs_phenomenon_10.svg https://upload.wikimedia.org/wikipedia/commons/f/f8/Gibbs_ph... So calculating it more like that is not a feature.
- smallnamespace 10y ago
  > A monitor does not quite deliver perfect squares, Monitors don't display colored squares, period: https://upload.wikimedia.org/wikipedia/commons/4/4d/Pixel_geometry_01_Pengo.jpg https://upload.wikimedia.org/wikipedia/commons/4/4d/Pixel_ge... Our cone cells also don't see colored squares, and in fact each color's distribution is random: https://askabiologist.asu.edu/sites/default/files/resources/articles/seecolor/model-retina-rods-cones-200.jpg https://askabiologist.asu.edu/sites/default/files/resources/... In fact, CRTs phosphors didn't even correspond to logical computer pixels. If your CRT resolution was lower than the maximum phosphor grid resolution of the CRT mask, then a single pixel would indeed spread across more than one tri-color phosphor group. Signal theory points reminds us that 'square pixels' are just an arbitrary shortcut. We could equally well describe them as hexagons, ovals, or rectangles, or make the grid positions random, and monitors would work just as well. That's why when you blow up a and render it as a giant square with exact edges, it's a very misleading and arbitrary choice.
  - lmm 10y ago
    But at no point, either in the CRT or in the human eye, do the ringing artifacts actually show up. So any pipeline that renders those when you blow the pixel up is worse than rendering just a giant square.
    - smallnamespace 10y ago
      They do. If you try to draw a white pixel in the middle of a black background on a CRT, the white bleeds around in a small circle, and if look at a point light source in a totally dark room, you will see a small halo around it. These are both ringing artifacts.
      - lmm 10y ago
        You see faint light around the pixel/light source. You don't see the edges of the pixel/light source as brighter than the center. Do you? (Can't check right now but it's not how I remember seeing things)

Dylan16807 10y ago

> That's not precisely true: discrete blocks or edges can be approximated arbitrarily closely in Fourier frequency space -- you just need to admit higher-frequency components. You can approximate those shapes, but that's an approximation. It's not impossible to do the math that way, but there are stumbling blocks to dodge. Like weird artifacts when you low-pass. > 'Pixel-sized square' is properly an oxymoron if you view pixels purely as samples -- a 'true' square can only be represented by an infinitely dense set of pixel samples. It's a square equal in size to the square-grid pixel spacing. It's not wrong, it's just being non-pedantic. > But this is a feature, not a bug, because neither computer monitors, nor the human eye, can render nor see a 'true' square either, only successively better approximations to them. A monitor does not quite deliver perfect squares, but what it displays is a lot closer to a square than to this shape: https://upload.wikimedia.org/wikipedia/commons/f/f8/Gibbs_phenomenon_10.svg https://upload.wikimedia.org/wikipedia/commons/f/f8/Gibbs_ph... So calculating it more like that is not a feature.

smallnamespace 10y ago
> A monitor does not quite deliver perfect squares, Monitors don't display colored squares, period: https://upload.wikimedia.org/wikipedia/commons/4/4d/Pixel_geometry_01_Pengo.jpg https://upload.wikimedia.org/wikipedia/commons/4/4d/Pixel_ge... Our cone cells also don't see colored squares, and in fact each color's distribution is random: https://askabiologist.asu.edu/sites/default/files/resources/articles/seecolor/model-retina-rods-cones-200.jpg https://askabiologist.asu.edu/sites/default/files/resources/... In fact, CRTs phosphors didn't even correspond to logical computer pixels. If your CRT resolution was lower than the maximum phosphor grid resolution of the CRT mask, then a single pixel would indeed spread across more than one tri-color phosphor group. Signal theory points reminds us that 'square pixels' are just an arbitrary shortcut. We could equally well describe them as hexagons, ovals, or rectangles, or make the grid positions random, and monitors would work just as well. That's why when you blow up a and render it as a giant square with exact edges, it's a very misleading and arbitrary choice.
- lmm 10y ago
  But at no point, either in the CRT or in the human eye, do the ringing artifacts actually show up. So any pipeline that renders those when you blow the pixel up is worse than rendering just a giant square.
  - smallnamespace 10y ago
    They do. If you try to draw a white pixel in the middle of a black background on a CRT, the white bleeds around in a small circle, and if look at a point light source in a totally dark room, you will see a small halo around it. These are both ringing artifacts.
    - lmm 10y ago
      You see faint light around the pixel/light source. You don't see the edges of the pixel/light source as brighter than the center. Do you? (Can't check right now but it's not how I remember seeing things)