Python program to create sphere coordinates not working

Question

I am trying to generate points that lies on the surface of a sphere centered on (0,0) in python.

# r - the radius of the sphere
def createSphere(r):
    lst = []
    for z in range(-r, r+1):

        r_ = r - abs(z)
        if r_ == 0:
            lst.append((0,0,r*np.sign(z)))
        else:
            for d in range(r_):
                lst.append((r_ * cos(d * (360/float(r_))), r_ * sin(d * 360/float(r_))), z)            )
    return lst

It will return a list [(x1,y1,z1),...].

This is how the result looks like:

The surface isn't smooth, and it looks kinda like a cube with extra sharp corners.

Does anyone know whats wrong?

Thanks

Answer 1

Use the standard spherical to cartesian coordinate transformation:

import math
pi = math.pi
sin = math.sin
cos = math.cos

def createSphere(r, N=10):
    lst = []
    thetas = [(2*pi*i)/N for i in range(N)]
    phis = [(pi*i)/N for i in range(N)]
    for theta in thetas:
        for phi in phis:
            x = r * sin(phi) * cos(theta)
            y = r * sin(phi) * sin(theta)
            z = r * cos(phi)
            lst.append((x, y, z))
    return lst

---

Per the comments below: If you wish to vary the number of points depending on the height (or phi), you could let thetas depend on phi:

def createSphere(r, N=10):
    lst = []
    for phi in [(pi*i)/(N-1) for i in range(N)]:
        M = int(sin(phi)*(N-1))+1
        for theta in [(2*pi*i)/M for i in range(M)]:
            x = r * sin(phi) * cos(theta)
            y = r * sin(phi) * sin(theta)
            z = r * cos(phi)
            lst.append((x, y, z))
    return lst

Above, the key line is

M = int(sin(phi)*(N-1))+1

M will equal 1 when phi is 0 or pi, and it will equal N when phi equals pi/2 (at the "equator"). Note that this is just one possible way to define M. Instead of using sin, you could instead define a piecewise linear function with the same boundary values, for example...