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name: hex-grid-spatial description: Hex grid spatial utilities for offset coordinate systems. Use when working with hexagonal grids, calculating distances, finding neighbors, or spatial queries on hex maps.

Hex Grid Spatial Utilities

Utilities for hexagonal grid coordinate systems using odd-r offset coordinates (odd rows shifted right).

Coordinate System

• Tile 0 is at bottom-left
• X increases rightward (columns)
• Y increases upward (rows)
• Odd rows (y % 2 == 1) are shifted right by half a hex

Direction Indices

     2   1
      \ /
   3 - * - 0
      / \
     4   5

0=East, 1=NE, 2=NW, 3=West, 4=SW, 5=SE

Core Functions

Get Neighbors

def get_neighbors(x: int, y: int) -> List[Tuple[int, int]]:
    """Get all 6 neighboring hex coordinates."""
    if y % 2 == 0:  # even row
        directions = [(1,0), (0,-1), (-1,-1), (-1,0), (-1,1), (0,1)]
    else:  # odd row - shifted right
        directions = [(1,0), (1,-1), (0,-1), (-1,0), (0,1), (1,1)]
    return [(x + dx, y + dy) for dx, dy in directions]

Hex Distance

def hex_distance(x1: int, y1: int, x2: int, y2: int) -> int:
    """Calculate hex distance using cube coordinate conversion."""
    def offset_to_cube(col, row):
        cx = col - (row - (row & 1)) // 2
        cz = row
        cy = -cx - cz
        return cx, cy, cz

    cx1, cy1, cz1 = offset_to_cube(x1, y1)
    cx2, cy2, cz2 = offset_to_cube(x2, y2)
    return (abs(cx1-cx2) + abs(cy1-cy2) + abs(cz1-cz2)) // 2

Tiles in Range

def get_tiles_in_range(x: int, y: int, radius: int) -> List[Tuple[int, int]]:
    """Get all tiles within radius (excluding center)."""
    tiles = []
    for dx in range(-radius, radius + 1):
        for dy in range(-radius, radius + 1):
            nx, ny = x + dx, y + dy
            if (nx, ny) != (x, y) and hex_distance(x, y, nx, ny) <= radius:
                tiles.append((nx, ny))
    return tiles

Usage Examples

# Find neighbors of tile (21, 13)
neighbors = get_neighbors(21, 13)
# For odd row: [(22,13), (22,12), (21,12), (20,13), (21,14), (22,14)]

# Calculate distance
dist = hex_distance(21, 13, 24, 13)  # Returns 3

# Check adjacency
is_adj = hex_distance(21, 13, 21, 14) == 1  # True

# Get all tiles within 3 of city center
workable = get_tiles_in_range(21, 13, 3)

Key Insight: Even vs Odd Row

The critical difference is in directions 1, 2, 4, 5 (the diagonal directions):

Direction	Even Row (y%2==0)	Odd Row (y%2==1)
NE (1)	(0, -1)	(1, -1)
NW (2)	(-1, -1)	(0, -1)
SW (4)	(-1, +1)	(0, +1)
SE (5)	(0, +1)	(1, +1)

East (0) and West (3) are always (1, 0) and (-1, 0).