Questions on MaterialGrid

[mawc2019]

According to the Meep documents, the grid points of MaterialGrid are defined at the corners of the voxels. Therefore, if we want to discretize a MaterialGrid region with a specified resolution, it seems that the numbers of grid points should be calculated like
Nx,Ny = int(resolution*width)+1,int(resolution*height)+1 instead of Nx,Ny = int(resolution*width),int(resolution*height).
In the latter case, the spacing between adjacent grid points is slightly different from 1/resolution, which means the actual resolution of the MaterialGrid is slightly different from the given resolution. But in the tutorials and built-in tests, Nx and Ny are computed as the latter expression. Is it a convention in Meep that resolution is defined according to the number of points rather than the number of intervals like 1/𐤃x?

Another question is related to periodic boundary conditions. If a MaterialGrid region extends across the periodic direction, e.g., the x direction, the grid points at the smallest-x boundary should always have the same weights as the grid points at the largest-x boundary because of periodicity, but why does MaterialGrid allow them to be different, or do I have misunderstanding here?

[stevengj]

Yes, the +1 form is correct. I think we recently changed some of the tutorials and/or tests to use this + 1, in fact?

[smartalecH]

I think we recently changed some of the tutorials and/or tests to use this + 1, in fact?

We actually changed it back to not using +1. See #2016

[stevengj]

Why was that?

[smartalecH]

As discussed today we should change it back -- sorry!

[stevengj]

Hmm, I can't find this; @oskooi, do you remember this change?

[mawc2019]

In addition, would it be better to replace expressions like int(Lx * resolution) and int(Ly * resolution) with int(round(Lx * resolution)) and int(round(Ly * resolution)) in cylindrical_filter, conic_filter, and gaussian_filter,@smartalecH ? The former expression sometimes produce unexpected results. For example, suppose resolution=40 and Lx=1+1/resolution+1/resolution. People may expect int(Lx * resolution) to be 42, but the result is 41, which can be demonstrated as follows.

resolution = 40
Lx = 1+1/resolution+1/resolution
print("int(Lx*resolution) = ",int(Lx*resolution))
print("int(round(Lx*resolution)) = ",int(round(Lx*resolution)))

The output is

int(Lx*resolution) =  41
int(round(Lx*resolution)) =  42

[mawc2019]

According to the Meep documents, the grid points are defined at the corners of the voxels, and the weights array is used to define a linear interpolation from medium1 to medium2. If so, even if the weights array becomes binarized, the refractive indices represented by weights may not be binarized in the regions between adjacent grid points with different weights values, i.e., 0 and 1. Do I have misunderstanding here?

[stevengj]

Remember that the projection happens after the linear interpolation, so it is still binary almost everywhere for β=∞.

However, when it is then discretized onto the Yee grid, there is subpixel smoothing.