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Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

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Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#81

Post by dahart »

rsp1984 wrote: post #79
dahart wrote: post #47

Earlier quoted context omitted.

It’s very useful to point out that it’s a Box Filter because the article moves on to using other filters, and larger clipping regions than a single pixel. This is framing the operation in known signal processing terminology, because that’s what you need to do in order to fully understand very high quality rendering. Dig a little further into the “bilinear filter” and “bicubic filter” that follow the box filter discus…

OK, I get it now. Thanks for the explanation. I would just never in a lifetime call it a "filter". That's extremely poor naming. If they called it a choice of basis or influence function, it would've been so much clearer.

Oh interesting, I hadn’t thought about it, but why does it seem like poor naming? I believe “filter” is totally standard in signal processing and has been for a long time, and that term does make sense to me in this case because what we’re trying to do is low-pass filter the signal, really. The filtering is achieve through convolution, and to your point I think there might be cases in which referring to the filter function as a basis function occurs.

I would think that conceptually that a basis function is different form a filter function because a basis function is usually about transforming a point in one space to some different space, and basis functions come in a set that’s the size of the dimensionality of the target space. Filters, even if you can think of the function as a sort of basis, aren’t meant for changing spaces or encoding & decoding against a different basis than the signal. Filters transform the signal but keep it in the same space it started from, and the filter is singular and might lose data.

May be better if I just link to what others say about filters than me trying to blabber on https://en.wikipedia.org/wiki/Filter_(signal_processing)

Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#82

Post by nyanpasu64 »

raphlinus wrote: post #66
mfabbri77 wrote: post #54

Earlier quoted context omitted.

As pointed out by Raphlinus, the moire pattern in the Siemens star isn't such a significant quality indicator for the type of content usually encountered in 2D vector graphics. With the analytical coverage calculation you can have perfect font/text rendering, perfect thin lines/shapes and, by solving all the areas at once, no conflating artifacts.

I don't see how you can support the claim of perfect thin line rendering, it's visibly just not very good. So box filtering logically can't possibly be the best possible quality. Can we make a magical adaptive filter which resembles box filter for half-planes, a tent filter for thin lines, Mitchell-Netravali or oblique projection for natural images, and Gaussian when filtering images for which high frequency detail i…

I wonder if the ideas behind GIMP's new nonlinear resampling filters (NoHalo and LoHalo, and eventually more https://graphicdesign.stackexchange.com/q/138059) may translate to vector rasterization in some form (though here we're translating continuous to discrete, not discrete to continuous to a differently spaced discrete).

Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#83

Post by nyanpasu64 »

adastra22 wrote: post #63
phkahler wrote: post #57

Earlier quoted context omitted.

Backing up to your earlier comment. Pixels on some displays are in fact little squares of uniform color . The question then is how to color a pixel given geometry with detail within that square. All of this "filtering" is variations on adding blur. In fact the article extends the technique to deliberately blur images on a larger scale. When we integrate a function (which could be a color gradient over a fully filled…

I don’t know of any display technology in which pixels are little squares, if you really get out the magnifying glass.

Would DLP projectors which distribute color over time (a color wheel) or multiple light sources combined with dichroic filters, produce uniform squares of color?

Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#84

Post by dahart »

nyanpasu64 wrote: post #83
adastra22 wrote: post #63

Earlier quoted context omitted.

I don’t know of any display technology in which pixels are little squares, if you really get out the magnifying glass.

Would DLP projectors which distribute color over time (a color wheel) or multiple light sources combined with dichroic filters, produce uniform squares of color?

In theory if the DMD mirrors were perfect little squares, and if the lens has perfect focus, and if the mirrors switch infinitely fast and are perfectly aligned with the color wheel in time, then maybe it’d be fair to call them uniform squares of color. In reality, the mirrors look square, but aren’t perfect squares - there’s variance in the flatness, aim, edges & beveling, and also both the lens and mirror switching blurs the pixels. The mirror switching over time is not infinitely fast, so the colors change during their cycle (usually multiple times per color of the wheel!) Not to mention some newer DLPs are using LEDs that are less square than DMD mirrors to begin with.

All this comes down to the projected pixels not being nearly as square as one might think (maybe that’s on purpose), though do note that squares are not the ideal shape of a pixel in the first place, for the same reason box filtering isn’t the best filter. If your pixel has sharp edges, that causes artifacts.

Take a look at the pixel-close-up comparisons in the projection shoot-out: https://www.projectorcentral.com/Projector-Resolution-Shooto...

Notice how all of them are visibly blurrier than the source image, and even that all of them have visible aliasing.

Also just for fun, check out this interesting video showing what DMD mirrors look like under a microscope: https://youtu.be/KpatWNi0__o

Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#85

Post by 3n_scanline »

For comparison, Tom Duff has just made available a copy of his 1989 paper "Polygon scan conversion by exact convolution" which uses more or less the same mathematical trick. It involves a scanline algorithm and avoids polygon clipping.

http://tomduff.com/conscan.pdf

Re: Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing

#86

Post by david-gpu »

adastra22 wrote: post #77
david-gpu wrote: post #73

Earlier quoted context omitted.

If only it was so simple. You typically don't have the memory capacity and computational budget to sort and render the whole scene back to front. You can use bucketing and other tricks to try and do a better job, but at the end of they day it is just impractical. This method has been studied for decades and it is still not in common use.

Are we still talking about 2D raster libraries (TFA)?

It makes no difference.
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