Module detector_spread 

Counts the detector records away from where they arrive.

The detector is a grid of square cells of side 1. Counts arrive evenly over a cell, and the share of them the detector spreads is recorded at a displacement u drawn from a radial kernel normalized over the plane,

K(r) = Σ_c w_c·exp(−r/s_c)/(2π s_c²),   Σ_c w_c = 1,

lengths s_c in cells. The share of a cell’s spread counts recorded in the cell offset by (dx, dy) is

T(dx, dy) = ∫ K(u)·Λ(u_x − dx)·Λ(u_y − dy) du,   Λ(t) = max(0, 1 − |t|),

Λ(u_x − dx)·Λ(u_y − dy) the overlap of the two cells displaced by u.

Functions

region_shares

F[r][q], the share of the spread counts arriving evenly over the cells of region q that the detector records in the cells of region r, for the regions’ cells cells as [row, column] on a grid of grid rows and columns. Counts spread to cells in no region, or off the grid, are not recorded in any region. Each region’s spread image is its cells convolved with T, by FFT on a grid padded so that no offset wraps.

transfer

T(dx, dy) of the kernel (w_c, s_c), weights normalized by their sum.