Faster way to calculate hexagon grid coordinates

Question

I'm using the following procedure to calculate hexagonal polygon coordinates of a given radius for a square grid of a given extent (lower left --> upper right):

def calc_polygons(startx, starty, endx, endy, radius):
    sl = (2 * radius) * math.tan(math.pi / 6)

    # calculate coordinates of the hexagon points
    p = sl * 0.5
    b = sl * math.cos(math.radians(30))
    w = b * 2
    h = 2 * sl


    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

This works well for polygons into the millions, but quickly slows down (and takes up very large amounts of memory) for large grids. I'm wondering whether there's a way to optimise this, possibly by zipping together numpy arrays of vertices that have been calculated based on the extents, and removing the loops altogether – my geometry isn't good enough for this, however, so any suggestions for improvements are welcome.

Answer 1

Decompose the problem into the regular square grids (not-contiguous). One list will contain all shifted hexes (i.e. the even rows) and the other will contain unshifted (straight) rows.

def calc_polygons_new(startx, starty, endx, endy, radius):
    sl = (2 * radius) * math.tan(math.pi / 6)

    # calculate coordinates of the hexagon points
    p = sl * 0.5
    b = sl * math.cos(math.radians(30))
    w = b * 2
    h = 2 * sl


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

    row = 1

    shifted_xs = []
    straight_xs = []
    shifted_ys = []
    straight_ys = []

    while startx < endx:
        xs = [startx, startx, startx + b, startx + w, startx + w, startx + b, startx]
        straight_xs.append(xs)
        shifted_xs.append([xoffset + x for x in xs])
        startx += w

    while starty < endy:
        ys = [starty + p, starty + (3 * p), starty + h, starty + (3 * p), starty + p, starty, starty + p]
        (straight_ys if row % 2 else shifted_ys).append(ys)
        starty += yoffset
        row += 1

    polygons = [zip(xs, ys) for xs in shifted_xs for ys in shifted_ys] + [zip(xs, ys) for xs in straight_xs for ys in straight_ys]
    return polygons

As you predicted, zipping results in much faster performance, especially for larger grids. On my laptop I saw 3x speedup when calculating 30 hexagon grid - 10x speed for 2900 hexagon grid.

>>> from timeit import Timer
>>> t_old = Timer('calc_polygons_orig(1, 1, 100, 100, 10)', 'from hexagons import calc_polygons_orig')
>>> t_new = Timer('calc_polygons_new(1, 1, 100, 100, 10)', 'from hexagons import calc_polygons_new')
>>> t_old.timeit(20000)
9.23395299911499
>>> t_new.timeit(20000)
3.12791109085083
>>> t_old_large = Timer('calc_polygons_orig(1, 1, 1000, 1000, 10)', 'from hexagons import calc_polygons_orig')
>>> t_new_large = Timer('calc_polygons_new(1, 1, 1000, 1000, 10)', 'from hexagons import calc_polygons_new')
>>> t_old_large.timeit(200)
9.09613299369812
>>> t_new_large.timeit(200)
0.7804560661315918

There might be an opportunity to create an iterator rather than the list to save memory. Depends on how your code is using the list of the polygons.