> but the author prefers point samples, which are easiest to do math on.
Easiest, and most correct, or at least a lot harder to screw up.
> The correctest interpretation depends on the sampling device
The “point-samples interpretation” is always perfectly correct, encompassing other definitions. The thing that differs from one device to another is the reconstruction filter used to interpret the meaning of those point samples. Given that a nearest-neighbor type reconstruction filter is pretty much never the best, using the “little square” interpretation that ties us down to that reconstruction is counterproductive.
> Ironically, modern technology uses rectangular spaced subpixels in both sampling and representation.
In sampling, I assume you mean the sensors in digital cameras? Treating them as squares/rectangles instead of point samples is not especially useful, because the optical system is pretty complicated, and so lens blur/chromatic aberration/etc. are at a larger scale than the pixels themselves. Better is to just wrap the knowledge of pixel shape and the knowledge of optical effects into the same part of the model, the reconstruction filter.
The point-sample interpretation is perfectly relevant for current-resolution devices. In the case of LCDs for example, you just have to keep in mind that the sample points for R, G, and B subpixels are not the same.
Easiest, and most correct, or at least a lot harder to screw up.
> The correctest interpretation depends on the sampling device
The “point-samples interpretation” is always perfectly correct, encompassing other definitions. The thing that differs from one device to another is the reconstruction filter used to interpret the meaning of those point samples. Given that a nearest-neighbor type reconstruction filter is pretty much never the best, using the “little square” interpretation that ties us down to that reconstruction is counterproductive.
> Ironically, modern technology uses rectangular spaced subpixels in both sampling and representation.
In sampling, I assume you mean the sensors in digital cameras? Treating them as squares/rectangles instead of point samples is not especially useful, because the optical system is pretty complicated, and so lens blur/chromatic aberration/etc. are at a larger scale than the pixels themselves. Better is to just wrap the knowledge of pixel shape and the knowledge of optical effects into the same part of the model, the reconstruction filter.
The point-sample interpretation is perfectly relevant for current-resolution devices. In the case of LCDs for example, you just have to keep in mind that the sample points for R, G, and B subpixels are not the same.