沿非均匀分布的圆柱面生成 3D 点

Question

I am trying to randomly generate points along the curved surface of a cylinder that has ay up-axis. Following a SO question of creating points along a 2D circle, I have

def point(h, k, r):
    theta = random.random() * 2 * pi
    global x
    global y
    x = h + cos(theta) * r
    y = k + sin(theta) * r

given the cylinder's (h,k) origin point (0, -21.56462) and r (radius = 7.625). I then made these points 3D by generating az point within my range (-2.35, 12.31). However, this got me half the way there because the final result was a cylinder but rotated 90 degrees clockwise.

Image of generated cylinder

What formula can I use that will generate the points in the correct direction? I am not that familiar with trigonometry, unfortunately. Thanks in advance!

THE SOLUTION:

def point(h, k, r):
    theta = random.random() * 2 * pi
    global x
    global z
    x = h + cos(theta) * r
    z = k + sin(theta) * r

The new (h,k) origin is now (x,z) where x and z are the coordinates for the center of the cylinder and y is randomly generated within its appropriate height range. The vector is still (x,y,z).

Updated generated cylinder

Answer 1

THE SOLUTION:

(thanks to David Huculak)

def point(h, k, r):
    theta = random.random() * 2 * pi
    global x
    global z
    x = h + cos(theta) * r
    z = k + sin(theta) * r

The new (h,k) origin is now (x,z) where x and z are the coordinates for the center of the cylinder and y is randomly generated within its appropriate height range. The vector is still (x,y,z).

Updated Generated cylinder