Python Math: Calculate a grid of hexagon coordinates of the given radius given lower-left and upper-right coordinates

Last update on April 24 2025 12:44:17 (UTC/GMT +8 hours)

62. Hexagon Grid Generator

Write a Python program to calculate a grid of hexagon coordinates of the given radius given lower-left and upper-right coordinates. The function will return a list of lists containing 6 tuples of x, y point coordinates. These can be used to construct valid regular hexagonal polygons.

Sample Solution:

Python Code:

#https://gist.github.com/urschrei/17cf0be92ca90a244a91
import math
def calculate_polygons(startx, starty, endx, endy, radius):
     # calculate side length given radius   
    sl = (2 * radius) * math.tan(math.pi / 6)
    # calculate radius for a given side-length
    # (a * (math.cos(math.pi / 6) / math.sin(math.pi / 6)) / 2)
    # see http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
    
    # calculate coordinates of the hexagon points
    # sin(30)	
    p = sl * 0.5
    b = sl * math.cos(math.radians(30))
    w = b * 2
    h = 2 * sl
    
    # offset start and end coordinates by hex widths and heights to guarantee coverage     
    startx = startx - w
    starty = starty - h
    endx = endx + w
    endy = endy + h

    origx = startx
    origy = starty


    # offsets for moving along and up rows
    xoffset = b
    yoffset = 3 * p

    polygons = []
    row = 1
    counter = 0

    while starty < endy:
        if row % 2 == 0:
            startx = origx + xoffset
        else:
            startx = origx
        while startx < endx:
            p1x = startx
            p1y = starty + p
            p2x = startx
            p2y = starty + (3 * p)
            p3x = startx + b
            p3y = starty + h
            p4x = startx + w
            p4y = starty + (3 * p)
            p5x = startx + w
            p5y = starty + p
            p6x = startx + b
            p6y = starty
            poly = [
                (p1x, p1y),
                (p2x, p2y),
                (p3x, p3y),
                (p4x, p4y),
                (p5x, p5y),
                (p6x, p6y),
                (p1x, p1y)]
            polygons.append(poly)
            counter += 1
            startx += w
        starty += yoffset
        row += 1
    return polygons

print(calculate_polygons(1,1, 4, 4, 3))

Sample Output:

[[(-5.0, -4.196152422706632), (-5.0, -0.7320508075688767), (-2.0, 1.0), (1.0, -0.7320508075688767), (1.0, -4.1
96152422706632), (-2.0, -5.928203230275509), (-5.0, -4.196152422706632)], [(1.0, -4.196152422706632), (1.0, -0
.7320508075688767), (4.0, 1.0), (7.0, -0.7320508075688767), (7.0, -4.196152422706632), (4.0, -5.92820323027550
9), (1.0, -4.196152422706632)], [(7.0, -4.196152422706632), (7.0, -0.7320508075688767), (10.0, 1.0), (13.0, -0
.7320508075688767), (13.0, -4.196152422706632), (10.0, -5.928203230275509), (7.0, -4.196152422706632)], [(-2.0
------
), (10.0, 14.85640646055102), (10.0, 11.392304845413264), (7.0, 9.660254037844387), (4.0, 11.392304845413264)]
]  

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to generate a grid of hexagon coordinates within specified lower-left and upper-right boundaries and print the list of hexagon vertices.
• Write a Python function that calculates the coordinates of a regular hexagon given a center and radius, then uses it to build a grid of hexagons.
• Write a Python script to compute hexagon vertices for multiple hexagons in a grid and verify that adjacent hexagons share common edges.
• Write a Python program to generate hexagon coordinates and then visualize the grid using matplotlib, ensuring all hexagons are regular.

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Python Code Editor:

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