球体上的点

Question

I am new in Python and I have a sphere of radius (R) and centred at (x0,y0,z0). Now, I need to find those points which are either on the surface of the sphere or inside the sphere eg points (x1,y1,z1) which satisfy ((x1-x0)**2+(y1-y0)**2+(z1-x0)*82)**1/2 <= R. I would like to print only those point's coordinates in a form of numpy array. Output would be something like this-[[x11,y11,z11],[x12,y12,z12],...]. I have the following code so far-

import numpy as np
import math

def create_points_around_atom(number,atom_coordinates):
    n= number
    x0 = atom_coordinates[0]
    y0 = atom_coordinates[1]
    z0 = atom_coordinates[2]
    R = 1.2
    for i in range(n):
        phi = np.random.uniform(0,2*np.pi,size=(n,))
        costheta = np.random.uniform(-1,1,size=(n,))
        u = np.random.uniform(0,1,size=(n,))
        theta = np.arccos(costheta)
        r = R * np.cbrt(u)
        x1 = r*np.sin(theta)*np.cos(phi) 
        y1 = r*np.sin(theta)*np.sin(phi)
        z1 = r*np.cos(theta)
        dist  = np.sqrt((x1-x0)**2+(y1-y0)**2+(z1-z0)**2)
        distance = list(dist)
        point_on_inside_sphere = []
        for j in distance:
            if j <= R:
                point_on_inside_sphere.append(j)
                print('j:',j,'\tR:',R)
                print('The list is:', point_on_inside_sphere)
                print(len(point_on_inside_sphere))
                kk =0
                for kk in range(len(point_on_inside_sphere)):
                    for jj in point_on_inside_sphere:
                        xx = np.sqrt(jj**2-y1**2-z1**2)
                        yy = np.sqrt(jj**2-x1**2-z1**2)
                        zz = np.sqrt(jj**2-y1**2-x1**2)
                    print("x:", xx, "y:", yy,"z:", zz)
                kk +=1 

And I am running it- create_points_around_atom(n=2,structure[1].coords) where, structure[1].coords is a numpy array of three coordinates.

Answer 1

To sum up what has been discussed in the comments, and some other points:

• There is no need to filter the points because u <= 1 , which means np.cbrt(u) <= 1 and hence r = R * np.cbrt(u) <= R , ie all points will already be inside or on the surface of the sphere.

• Calling np.random.uniform with size=(n,) creates an array of n elements, so there's no need to do this n times in a loop.

• You are filtering distances from the atom_coordinate , but the points you are generating are centered on [0, 0, 0] , because you are not adding this offset.

• Passing R as an argument seems more sensible than hard-coding it.

• There's no need to "pre-load" arguments in Python like one would sometimes do in C.

• Since sin(theta) is non-negative over the sphere, you can directly calculate it from the costheta array using the identity cos²(x) + sin²(x) = 1 .

Sample implementation:

# pass radius as an argument
def create_points_around_atom(number, center, radius):

    # generate the random quantities
    phi         = np.random.uniform( 0, 2*np.pi, size=(number,))
    theta_cos   = np.random.uniform(-1,       1, size=(number,))
    u           = np.random.uniform( 0,       1, size=(number,))

    # calculate sin(theta) from cos(theta)
    theta_sin   = np.sqrt(1 - theta_cos**2)
    r           = radius * np.cbrt(u)

    # use list comprehension to generate the coordinate array without a loop
    # don't forget to offset by the atom's position (center)
    return np.array([
        np.array([
            center[0] + r[i] * theta_sin[i] * np.cos(phi[i]),
            center[1] + r[i] * theta_sin[i] * np.sin(phi[i]),
            center[2] + r[i] * theta_cos[i]
        ]) for i in range(number)
    ])