Hexagonal Grids

Hexagonal grids use three coordinate systems—offset, cube, and axial—each suited to different algorithms. Start with axial coordinates for simplicity, convert to cube for pathfinding and distance calculations, then use offset for rendering. This Skill provides formulas for all three systems and conversions between them.

Hex distance uses the max-difference formula on cube coordinates: distance equals the maximum of the absolute differences across all three axes. Convert your coordinates to cube format, apply the formula, and you have the distance. This method is faster than Euclidean calculations and handles all hex orientations.

A* pathfinding on hex grids requires neighbor queries and hex distance heuristics. Convert coordinates to cube format, query the six neighbors of each hex, and use hex distance as your heuristic function. This Skill includes A* pathfinding examples and neighbor-finding algorithms for all coordinate systems.

Yes. Line drawing traverses hexes between two points using coordinate interpolation. Ring generation creates all hexes at a fixed distance from a center; spiral generation expands outward in rings. This Skill provides algorithms for both, handling edge cases and orientation variations.

Rendering typically uses offset or doubled coordinates, which map directly to screen pixels. Offset coordinates are the most intuitive for 2D arrays; doubled coordinates avoid fractional values. This Skill covers pixel-to-hex and hex-to-pixel conversions for both systems and handles even/odd row and column parity.

Yes. Hexagons can be oriented pointy-top or flat-top, and grids can use even or odd parity. This Skill handles orientation and parity variations across all coordinate systems, coordinate conversions, distance calculations, and rendering, ensuring robust support regardless of your map design.