AA/AF enhancements

[Simon F]

But the patterns shown above are not a solutions to N-queens, since two diagonals have attacking queens.

BTW, do you have any references to a proof that the N-queens solutions are optimal sampling patterns for N-by-N sparse grids?.

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

 

[K.I.L.E.R]

I've seen more references to the N Passant.

Seriously, why mix chess with AA sampling patterns?

But the patterns shown above are not a solutions to N-queens, since two diagonals have attacking queens.

BTW, do you have any references to a proof that the N-queens solutions are optimal sampling patterns for N-by-N sparse grids?.

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

 

[Simon F]

I've seen more references to the N Passant.

I must admit that was quite witty.

Seriously, why mix chess with AA sampling patterns?

It's all an attempt to avoid correlation between the samples. Assuming we are restricted to sample points that lie on some sub-grid (which is likely for cost reasons), then if you solve the N-Rook problem, for example, then you have spread your samples (within a pixel) over all N-Rows and all N-Columns of your sub grid.

So why do we want to avoid correlation? Well, sampling a signal that contains high frequencies (eg edges of polys or textures) will result in aliasing. With a regular grid this aliasing appears as low frequency noise which is easy to spot. A random Poisson-disc sample pattern, OTOH, shifts that aliasing into higher frequency noise, which is much harder to see. These N-Rook/N-Queen patterns are more like Poisson patterns.

 

[K.I.L.E.R]

Thanks.

Now I see where you guys are going.

I can be witty from time to time. Usually I'm just plain silly.

 

[Pavlos]

BTW, do you have any references to a proof that the N-queens solutions are optimal sampling patterns for N-by-N sparse grids?

In theory, the only thing we can prove about sparse grid/stratified sampling is that it will never give worst results than random sampling (completely random sample positions). We are using them because in practice they give better results for edge antialiasing. This is covered in many Monte Carlo text books and class notes.

The problem with n-rooks is that some solutions tend to give high correlation between the samples. On the other hand the N-queens solutions seem to produce better patterns and I think they are approximating the poison distribution better. Actually I’m going to improve the stochastic antialiasing of my renderer in the next release, so I will do some tests between the N-rooks and the N-queens solutions.

But in any case the “a-bufferâ€￾ gives better results faster. The cost of 64x antialiasing is only 3 bitwise XORs per visible triangles on the edges and some memory lookups. This will probably beat even hardware accelerated supersampling in some cases. I was really astonished by the speed of an early unoptimized implementation of the algorithm.

The SRT Rendering Toolkit

 

[OpenGL guy]

But the patterns shown above are not a solutions to N-queens, since two diagonals have attacking queens.

BTW, do you have any references to a proof that the N-queens solutions are optimal sampling patterns for N-by-N sparse grids?.

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally. For example, you wouldn't want sample positions like:

X...
.X..
..X.
...X

 

[Simon F]

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally. For example, you wouldn't want sample positions like:

X...
.X..
..X.
...X

Oh, I don't disagree with you, it was just that the references I saw mentioned the N-rooks problem. It was more a comment of amazement

 

[K.I.L.E.R]

I still think we should add (a copy of) QCX AA on the R3xx.

 

[EasyRaider]

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally.

:?

It's a while since I played chess...

but I'm pretty sure rooks can only attack diagonally.

 

[EasyRaider]

I still think we should add (a copy of) QCX AA on the R3xx.

Bah! Quincunx sux!

Hm... come to think of it, I have a GF4, but I've never tried the mode...

 

[K.I.L.E.R]

GL Guy is rusty on his Chess skills and knowledge. I bet I can beat him blindfolded in a game of chess.

BTW: QCX doesn't suck, your vision sucks.

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally.

:?

It's a while since I played chess...

but I'm pretty sure rooks can only attack diagonally.

 

[incurable]

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally.

:?

It's a while since I played chess...

but I'm pretty sure rooks can only attack diagonally.

Having played some chess in my youth, too, I seem to remember the bishops moving (and attacking) diagonally while the rooks were -errr- straight.

But then again, who'd trust a person that gave up chess club because it interfered with watching ST: TNG?

cu

incurable

 

[Althornin]

teh powar of google is strong in you!
FIDE Chess Rules
I cant believe you geeks dont know how a rook can or cant move

 

[Simon F]

I cant believe you geeks dont know how a rook can or cant move

Clearly, they have just forfeited their geek membership.

 

[tEd]

I still think we should add (a copy of) QCX AA on the R3xx.

yeah and while we are at it we also should copy nv's 6xs mode to r3xx because it so damn rocks

..or i just could wear my dirty glasses and have quincunx for free on r3xx hardware...

 

[digitalwanderer]

How would you apply castling to AA... (Been a while since I even thought about chess!)

 

[Randell]

GL Guy is rusty on his Chess skills and knowledge. I bet I can beat him blindfolded in a game of chess.

BTW: QCX doesn't suck, your vision sucks.

Actually, come to think of it, most of the references to AA that I've seen talk about the N-Rook problem instead.

You should use queens as rooks can't attack diagonally.

:?

It's a while since I played chess...

but I'm pretty sure rooks can only attack diagonally.

jeez, two people who don't know chess moves on a geek board..

 

[EasyRaider]

In my mind, I confused rook with pawn!



It really must be too long since I played chess...

Well, I guess the fact that English is not my native language is the real reason.

 

[K.I.L.E.R]

I'm a master chess player and can kick all your asses.

 

[OpenGL guy]

GL Guy is rusty on his Chess skills and knowledge. I bet I can beat him blindfolded in a game of chess.

It's a while since I played chess...

but I'm pretty sure rooks can only attack diagonally.

If you think rooks attack diagonally, I think your chances of beating me are pretty slim

P.S. I played tournament chess for about 7 years while I was in grad. school.

Edit: Fix typo.