Hexruudukot

Hexruudukot, commonly referred to as hex grids, are tilings of the plane by regular hexagons arranged so that every cell has six neighbors. This honeycomb pattern provides six-directional movement and compact, isotropic spacing, making hex grids popular for modeling space in board games, digital games, geographic information systems, and robotics.

There are two common hex orientations: pointy-topped, where a vertex points upward, and flat-topped, where a side is horizontal. The orientation affects how coordinates are assigned and how rows or columns align, influencing neighbor enumeration and drawing algorithms.

Several coordinate systems are used to index hex cells. Axial coordinates use two axes (q, r) that align with two of the six directions. Cube coordinates use three axes (x, y, z) with x + y + z = 0, which simplifies distance calculations. Offset coordinates map hexes to a square grid by shifting every other row or column (e.g., even-q, odd-q, even-r, odd-r). All systems have six valid neighbors corresponding to the six directions around a hex.

Distance between hexes can be computed in cube coordinates as max(|dx|, |dy|, |dz|). In axial coordinates, distance often equals (|dq| + |dr| + |dq + dr|) / 2. This makes pathfinding, such as A*, straightforward, since distance metrics reflect true hex steps.

Applications include strategy and role-playing games, terrain mapping, and procedural generation. Implementations typically store grid data in arrays or hash maps, use axial or cube coordinates for neighbor queries, and convert between coordinate systems as needed for rendering or intersection tests.