Placing spheres of known volume fraction using Random Sequential Adsorption algorithm.

RSA_spheres.py

"""
This module places spheres of known radius and volume fraction
in a cube of known min and max bounds using 
Random Sequential Adsorption (RSA) logic.

"""
import numpy as np
from math import pi

def rsa_spheres(r,vf,bounds, min_sep=0.00, max_attempts=1000):
    x_min, y_min, z_min, x_max, y_max, z_max = bounds
    lx, ly, lz = x_max-x_min, y_max-y_min, z_max-z_min
    num_sph = int((vf * (lx*ly*lz)) / ((4/3)*pi*r*r*r))
    #
    xyz = np.array([]).reshape(0,3)
    for i in range(num_sph):
        counter = 0
        while True:
            counter += 1
            #
            if counter>max_attempts:
                raise ValueError("Couldn't find non-overlapping sphere with in {} max_attempts".format(counter))
            #
            # get the new random sphere location
            new_xyz = [[x_min, y_min, z_min]] + ([lx, ly, lz]*np.random.rand(3))
            # check the overlap flag with accepted spheres
            overlap_flags = [(np.linalg.norm(a_xyz-new_xyz) < (r+min_sep+r)) for a_xyz in xyz]
            if any(overlap_flags):
                continue
            else:
                xyz = np.concatenate([xyz, new_xyz], axis=0)
                print("placed the sphere #{0}/{3} at {1} after {2} attempts".format(i+1, new_xyz, counter, num_sph))
                break
    #
    if xyz.shape[0]==num_sph:
        print("\n\t--- All {} spheres are placed ---".format(num_sph))
    return xyz
#
# Example::
radius=0.1  # radius
vol_fraction = 0.35  # volume fraction
rve_bounds = (-0.5, -0.5, -0.5, 0.5, 0.5, 0.5)
min_separation = 0.00 # times the radius, minimum separation between spheres
spheres_xyz = rsa_spheres(radius, vol_fraction, rve_bounds, min_sep=min_separation, max_attempts=1500)
print(spheres_xyz)