# 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.

# Expected Output :
[[(-5.0, -4.196152422706632), (-5.0, -0.7320508075688767), (-2.0, 1.0), (1.0, -0.
7320508075688767), (1.0, -4.196152422706632), (-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, -5.92820323
0275509), (1.0, -4.196152422706632)], [(7.0, -4.196152422706632), (7.0, -0.732050
8075688767), (10.0, 1.0), (13.0, -0.7320508075688767), (13.0, -4.196152422706632)
........                                  
(7.0, 9.660254037844387), (4.0, 11.392304845413264)]] 

import math  
#https://gist.github.com/urschrei/17cf0be92ca90a244a91  
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))