what algorithm 8xmsaa & 16xmsaa use to generate the position of 8 points& 16 points

Question

enter image description here

I want to know what pattern the point position is. i dont find the law of these eight points

Answer 1

Those are the standard DirectX MSAA sampling patterns. Even though there can be other sampling patterns, these are required for any DirectX 10 compliant card (and later versions as well).

Apparently Vulkan has adopted the same sampling patterns.

I don't know how Microsoft came up with those patterns though.

An interesting observation is that no 2 points lay on the same row or column. That makes me think it could be inspired by matrix determinant multiplications, but this is just speculation.

Looks like when no 2 samples lay on the same column or row it's called N-rooks (named after chess piece). Thanks @krOoze for the call.

I have found some interesting info about N-rooks in the book "Real Time Rendering 4th ed":

N-rooks is a family of sampling patters. Inside this family, some patterns are better than others.

For example, filling the diagonal is considered a bad placement.

There is a subfamily of N-rooks which is called RGSS (Rotated Grid Super Sampling)

Quoting the book:

The RGSS pattern is a form of Latin hypercube or N-rooks sampling, in which n samples are placed in an n×n grid, with one sample per row and column

The RGSS 4-rooks pattern looks exactly like the 2x2 pattern that Vulkan uses.

Quoting the book:

We also want a uniform distribution, spreading samples evenly over the area. To form such patterns, stratified sampling techniques such as Latin hypercube sampling are combined with other methods such as jittering, Halton sequences, and Poisson disk sampling [1413, 1758]. In practice GPU manufacturers usually hard-wire such sampling patterns into their hardware for multisampling antialiasing.

So the sampling standard pattern used in Vulkan and DirectX are probably just something found randomly that met certain desirable properties (such as N-rooks, evenly distributed in the area, etc). And now the are hard-wired in hardware.