__author__ = 'thoth'

# http://blender.stackexchange.com/questions/71179/script-for-hexagonal-distribution/71193

# https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres

# Fill a rectangular prism with cannonballs according to hexagonal close-packed (triangular orthobicupola variant).

# An alternate orientation not supported by this code is face-centered
# cubic which is geometrically similar, just aligned to a different axis.


import bpy
from math import *

def construct_cannonball(mesh, x,y,z):
    scn = bpy.context.scene

    obj = bpy.data.objects.new("ball", mesh)
    scn.objects.link(obj)

    obj.location = [x,y,z]


def mission1(mesh, r, xyz1, xyz2, construct_cannonball=construct_cannonball):

    dx = 2*r
    dy = sqrt(0.75)*dx

    dz = sqrt(2/3)*dx   # thank you, CRC Concise Encyclopedia of Mathematics

    w = 0
    z=xyz1[2]
    while z<xyz2[2]:

        v=0
        y=xyz1[1]
        if 1==w%2:
            y += dx/2 * tan(pi/6)
        while y < xyz2[1]:
            x = xyz1[0]
            if 1==w%2:
                if 1==v%2:
                    x -= dx/2 / cos(pi/6)
                else:
                    x += dx/2 / cos(pi/6)
            if 1 == v%2:
                x += dx/2
            while x < xyz2[0]:
                construct_cannonball(mesh, x,y,z)
                x += dx

            y += dy
            v+=1

        z += dz
        w += 1


def purge(scn, prefix):
    for obj in scn.objects:
        if obj.name[0:len(prefix)] == prefix:
            obj.name = "discard"
            scn.objects.unlink(obj)

purge(bpy.context.scene, "ball")

mission1(bpy.data.objects['prototype'].data,
         1, [-5,-5,-5], [5,5,5])