title: Faster way to calculate hexagon grid coordinates
body: <p>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):</p>
  
  <pre><code>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 &lt; endy:
          if row % 2 == 0:
              startx = origx + xoffset
          else:
              startx = origx
          while startx &lt; 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
  </code></pre>
  
  <p>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.</p>