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

Last update on May 28 2022 13:45:53 (UTC/GMT +8 hours)

Python Math: Exercise-62 with Solution

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 https://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)]
]

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

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Find current directory and file's directory:

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import os dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

The os and os.path modules.

The __file__ constant

os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")

os.path.dirname(path) (returns "the directory name of pathname path")

os.getcwd() (returns "a string representing the current working directory")

os.chdir(path) ("change the current working directory to path")

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