hex_math.py

# hexagonal coordinates

# three coordinates are used in 2 dimensional space
# r - radius, measured in tiles along one of six spokes.
# a * 60 = angle.  a selects which spoke to transverse starting with 0 being north, and rotating counter-clockwise
# b - beta - moving at an angle of 120 degrees from "a", and counts in the python iterator range(r)

# for example, team A is at coordinates (rmax, 0, b) for b in range(2).
# then teams B and C are at (rmax, 2, b) and (rmax, 4, b).
# there is redundancy since the coordinates are over determined.
# for example, (rmax, 0, rmax) = (rmax, 1, 0).
# for example, (0, 0, 0), (rmax, 1, 0), (rmax, 2, 0) form an equal lateral triangle.

# tiles are numbered from 1 which is at hex location (0, 0, 0) which is at cx, cy.
# tile 1 is at

from math import pi, sin, cos, sqrt
t_height = 100


# trig functions using hexagonal angle (modulo 6)
def hsin(alpha): return sin(alpha * 60 * pi / 180)
def hcos(alpha): return cos(alpha * 60 * pi / 180)

def tile_generation(rmax, t_height):
    result = []
    tile = 0
    for r in range(rmax):
        for alpha in range(6 if r > 0 else 1):
            brange = r if r > 0 else 1
            #brange = 1   # testing
            for b in range(brange):
                x = t_height * (-r * hsin(alpha) - b * hsin(alpha + 2))
                y = t_height * (-r * hcos(alpha) - b * hcos(alpha + 2))
                result.append((tile, (r, alpha, b), (x, y)))
                tile += 1
    return result

if __name__ == "__main__":
    hex_tile_spec = tile_generation(4, t_height)
    for tile_spec in hex_tile_spec:
        tile, rab, xy = tile_spec
        r, alpha, b, x, y = rab + xy
        length = sqrt(x**2 + y**2)
        print(f'{tile}\t({r}, {alpha}, {b})\t({x:.2f}, {y:.2f}), len={length:.2f}')