CENTER algorithm - akilmarshall/procedural-image-generation GitHub Wiki

Fix $\left(1, 1\right)$ in $\mathcal{F}$ with $t_i$

    \mathcal{F}_{(1, 1, t_i)}=
    \begin{bmatrix}
    & & \\
    & t_i & \\
    & &
    \end{bmatrix}

The $CENTER$ algorithm expands a fragment of the form $\mathcal{F}_{(1, 1, t)}$

    CENTER\langle\mathcal{F}_{(1, 1, t)}\rangle=
    \begin{bmatrix}
    G=\mathcal{N}(c, 1)\cap \mathcal{N}(b, 2)  & B=\mathcal{N}(t,1) & F=\mathcal{N}(b, 0)\cap \mathcal{N}(a, 1) \\
    C=\mathcal{N}(t,2) & t & A=\mathcal{N}(t,0) \\
    H=\mathcal{N}(c, 3)\cap \mathcal{N}(d, 2) & D=\mathcal{N}(t,3) & E=\mathcal{N}(d, 0)\cap \mathcal{N}(a, 3)
    \end{bmatrix}

The $CENTER$ algorithm takes two steps:

1. Compute $\{A, B, C, D\}$ from $t_i$ directly
   1. select $\{a, b, c, d\}$ from $\{A, B, C, D\}$ respectively.
2. Compute $\{E, F, G, H\}$ from $\mathcal{N}(d, 0)\cap\mathcal{N}(a, 3)$, $\mathcal{N}(b, 0)\cap\mathcal{N}(a, 1)$, $\mathcal{N}(c, 1)\cap\mathcal{N}(b, 2)$ and, $\mathcal{N}(c, 3)\cap\mathcal{N}(d, 2)$ respectively
   1. select $\{e, f, g, h\}$ from $\{E, F, G, H\}$ respectively.