Python checking if a point is in sphere with center x, y ,z

Question

I'm trying to check if a point is within a sphere with a center point of (x, y, z) where (x, y, z) is not (0, 0, 0).

This code I'm using to generate the points I want to check:

def generatecoords(self, i):
    x, y, z = generatepoint()

    if i >= 1:
        valid = False

        while valid == False:
            coords = self.checkpoint(x, y, z)

            for b in world.starlist:
                if coords == world.starlist[b].coords:
                    coords = self.checkpoint(x, y, z)

                else:
                    valid = True

    else:
        coords = self.checkpoint(x, y, z)

    return coords

def checkpoint(self, x, y, z):
    d = math.sqrt(x * x + y * y + z * z)

    while d >= self.radius:
        x, y, z = generatepoint()
        d = math.sqrt(x * x + y * y + z * z)

    coords = (int(x), int(y), int(z))

    return coords

def generatepoint():
    x, y, z = [int(random.uniform(-self.radius, self.radius)) \
               for b in range(3)]

    return x, y, z

These function are called in a for loop to generate the points in a dictionary, while also checking the unlikely chance that points aren't placed on top of another(mostly because I can).

I trying to figure out what I need to add to math.sqrt(x * x + y * y + z * z) so that it accounts for a center that isn't (0, 0, 0). I do know of one way to do it, but it would require several lines of code and I'd rather do it in one. I would have asked this in the comments of the answer in another question, but I'm not allowed to comment on answers yet.

Answer 1

The formula is:

A point (x,y,z) is inside the sphere with center (cx,cy,cz) and radius r if

 (x - cx)^2 + (y - cy)^2 + (z - cz)^2 < r^2