Function assign_grid 

pub fn assign_grid(
    quads: &[LinkedQuad],
    component: &[usize],
) -> HashMap<usize, QuadGrid>

Propagate integer board-lattice coordinates across one connected component.

The seed quad is placed at the unit cell [(0,0),(1,0),(1,1),(0,1)]; each neighbor is positioned so its shared corner matches the already-assigned lattice coordinate, exploiting the fact that every quad shares the same rotational corner order (so a quad’s corners are always a translated unit cell in lattice space). Returns the per-quad lattice coordinates keyed by quad index.

Corners must already be ordered (order_all_corners).