Module space_filling 

Space-filling curves and locality-preserving orders: Hilbert (2-D and 3-D), Peano, Morton/Z-order, Gray codes, and L-system curves (Sierpiński arrowhead, Moore, Gosper).

Functions

gosper_curve

Gosper (flowsnake) curve, unit steps.

gray_code

Binary reflected Gray code.

gray_decode

Inverse Gray code (prefix xor by doubling).

hilbert_3d_d2xyz

3-D Hilbert index to grid coordinates on a 2^order cube.

hilbert_3d_xyz2d

3-D grid coordinates to Hilbert index (inverse of hilbert_3d_d2xyz).

hilbert_curve_2d

The full Hilbert curve as points in the unit square (cell centers), in curve order.

hilbert_curve_3d

The 3-D Hilbert curve as points in the unit cube, in curve order.

hilbert_d2xy

Hilbert curve index to grid coordinates on a 2^order square grid (Wikipedia’s iterative rotate-and-flip formulation).

hilbert_locality_ratio

Locality measure of the Hilbert order: mean |index difference| (normalized by the index range) divided by mean spatial distance (normalized by the bounding-box diagonal) over all point pairs. Lower means indices track spatial proximity better.

hilbert_xy2d

Grid coordinates to Hilbert index (inverse of hilbert_d2xy).

moore_curve

Moore curve: the closed variant of the Hilbert curve (last point adjacent to the first), unit grid steps.

morton_decode_2d

Inverse of morton_encode_2d.

morton_decode_3d

Inverse of morton_encode_3d.

morton_encode_2d

Interleaves the bits of x (even positions) and y (odd positions).

morton_encode_3d

Interleaves 21 bits each of x, y, z.

peano_curve

Peano curve on a 3^order grid via the ternary digit formula (Peano 1890): points in the unit square in curve order.

sierpinski_curve

Sierpiński arrowhead curve (traverses the Sierpiński triangle), unit steps from the origin.

sort_by_hilbert

Sorts points by their Hilbert index on a 2^order grid over the bounding box.

sort_by_morton

Sorts 3-D points by Morton code (21 bits per axis over the bounding box).

z_order_curve

The Z-order (Morton) traversal of a 2^order grid as unit-square points.