3D spinning donut in Python. Based on the pseudocode from: https://www.a1k0n.net/2011/07/20/donut-math.html

donut.py

import numpy as np

screen_size = 40
theta_spacing = 0.07
phi_spacing = 0.02
illumination = np.fromiter(".,-~:;=!*#$@", dtype="<U1")

A = 1
B = 1
R1 = 1
R2 = 2
K2 = 5
K1 = screen_size * K2 * 3 / (8 * (R1 + R2))


def render_frame(A: float, B: float) -> np.ndarray:
    """
    Returns a frame of the spinning 3D donut.
    Based on the pseudocode from: https://www.a1k0n.net/2011/07/20/donut-math.html
    """
    cos_A = np.cos(A)
    sin_A = np.sin(A)
    cos_B = np.cos(B)
    sin_B = np.sin(B)

    output = np.full((screen_size, screen_size), " ")  # (40, 40)
    zbuffer = np.zeros((screen_size, screen_size))  # (40, 40)

    cos_phi = np.cos(phi := np.arange(0, 2 * np.pi, phi_spacing))  # (315,)
    sin_phi = np.sin(phi)  # (315,)
    cos_theta = np.cos(theta := np.arange(0, 2 * np.pi, theta_spacing))  # (90,)
    sin_theta = np.sin(theta)  # (90,)
    circle_x = R2 + R1 * cos_theta  # (90,)
    circle_y = R1 * sin_theta  # (90,)

    x = (np.outer(cos_B * cos_phi + sin_A * sin_B * sin_phi, circle_x) - circle_y * cos_A * sin_B).T  # (90, 315)
    y = (np.outer(sin_B * cos_phi - sin_A * cos_B * sin_phi, circle_x) + circle_y * cos_A * cos_B).T  # (90, 315)
    z = ((K2 + cos_A * np.outer(sin_phi, circle_x)) + circle_y * sin_A).T  # (90, 315)
    ooz = np.reciprocal(z)  # Calculates 1/z
    xp = (screen_size / 2 + K1 * ooz * x).astype(int)  # (90, 315)
    yp = (screen_size / 2 - K1 * ooz * y).astype(int)  # (90, 315)
    L1 = (((np.outer(cos_phi, cos_theta) * sin_B) - cos_A * np.outer(sin_phi, cos_theta)) - sin_A * sin_theta)  # (315, 90)
    L2 = cos_B * (cos_A * sin_theta - np.outer(sin_phi, cos_theta * sin_A))  # (315, 90)
    L = np.around(((L1 + L2) * 8)).astype(int).T  # (90, 315)
    mask_L = L >= 0  # (90, 315)
    chars = illumination[L]  # (90, 315)

    for i in range(90):
        mask = mask_L[i] & (ooz[i] > zbuffer[xp[i], yp[i]])  # (315,)

        zbuffer[xp[i], yp[i]] = np.where(mask, ooz[i], zbuffer[xp[i], yp[i]])
        output[xp[i], yp[i]] = np.where(mask, chars[i], output[xp[i], yp[i]])

    return output


def pprint(array: np.ndarray) -> None:
    """Pretty print the frame."""
    print(*[" ".join(row) for row in array], sep="\n")


if __name__ == "__main__":
    for _ in range(screen_size * screen_size):
        A += theta_spacing
        B += phi_spacing
        print("\x1b[H")
        pprint(render_frame(A, B))

@Duxedough

Is there a way to slow down the donut? Mine is spinning like a BeyBlade.

For sure! Follow this instructions:

1. Import sleep function from time module.

import numpy as np
from time import sleep  # Add this module

# Rest of the code [...]

2. Add sleep function in loop.

# [...] Rest of the code ^

if __name__ == "__main__":
    for _ in range(screen_size * screen_size):
        A += theta_spacing
        B += phi_spacing
        print("\x1b[H")
        pprint(render_frame(A, B))
        sleep(0.05)                # Add sleep funcion here!
                                   # Try diffrent seconds!

Complete "slowed" code :

import numpy as np
from time import sleep  

screen_size = 40
theta_spacing = 0.07
phi_spacing = 0.02
illumination = np.fromiter(".,-~:;=!*#$@", dtype="<U1")

A = 1
B = 1
R1 = 1
R2 = 2
K2 = 5
K1 = screen_size * K2 * 3 / (8 * (R1 + R2))


def render_frame(A: float, B: float) -> np.ndarray:
    """
    Returns a frame of the spinning 3D donut.
    Based on the pseudocode from: https://www.a1k0n.net/2011/07/20/donut-math.html
    """
    cos_A = np.cos(A)
    sin_A = np.sin(A)
    cos_B = np.cos(B)
    sin_B = np.sin(B)

    output = np.full((screen_size, screen_size), " ")  # (40, 40)
    zbuffer = np.zeros((screen_size, screen_size))  # (40, 40)

    cos_phi = np.cos(phi := np.arange(0, 2 * np.pi, phi_spacing))  # (315,)
    sin_phi = np.sin(phi)  # (315,)
    cos_theta = np.cos(theta := np.arange(0, 2 * np.pi, theta_spacing))  # (90,)
    sin_theta = np.sin(theta)  # (90,)
    circle_x = R2 + R1 * cos_theta  # (90,)
    circle_y = R1 * sin_theta  # (90,)

    x = (np.outer(cos_B * cos_phi + sin_A * sin_B * sin_phi, circle_x) - circle_y * cos_A * sin_B).T  # (90, 315)
    y = (np.outer(sin_B * cos_phi - sin_A * cos_B * sin_phi, circle_x) + circle_y * cos_A * cos_B).T  # (90, 315)
    z = ((K2 + cos_A * np.outer(sin_phi, circle_x)) + circle_y * sin_A).T  # (90, 315)
    ooz = np.reciprocal(z)  # Calculates 1/z
    xp = (screen_size / 2 + K1 * ooz * x).astype(int)  # (90, 315)
    yp = (screen_size / 2 - K1 * ooz * y).astype(int)  # (90, 315)
    L1 = (((np.outer(cos_phi, cos_theta) * sin_B) - cos_A * np.outer(sin_phi, cos_theta)) - sin_A * sin_theta)  # (315, 90)
    L2 = cos_B * (cos_A * sin_theta - np.outer(sin_phi, cos_theta * sin_A))  # (315, 90)
    L = np.around(((L1 + L2) * 8)).astype(int).T  # (90, 315)
    mask_L = L >= 0  # (90, 315)
    chars = illumination[L]  # (90, 315)

    for i in range(90):
        mask = mask_L[i] & (ooz[i] > zbuffer[xp[i], yp[i]])  # (315,)

        zbuffer[xp[i], yp[i]] = np.where(mask, ooz[i], zbuffer[xp[i], yp[i]])
        output[xp[i], yp[i]] = np.where(mask, chars[i], output[xp[i], yp[i]])

    return output


def pprint(array: np.ndarray) -> None:
    """Pretty print the frame."""
    print(*[" ".join(row) for row in array], sep="\n")


if __name__ == "__main__":
    for _ in range(screen_size * screen_size):
        A += theta_spacing
        B += phi_spacing
        print("\x1b[H")
        pprint(render_frame(A, B))
        sleep(0.05)                # Add sleep funcion here!
                                   # Try diffrent seconds!

Thank you very much, iijwpy! I enjoy my donut much better now. Stay blessed!

miih cant run it

My doughnut is not spinning :(. I'm getting snapshots for each timestamp.

if youre using VS code , then you have to put the terminal on fullscreen when you run the code. (click the red circled button in the pic attached). And it runs smoothly

for me terminal dosent show up anything after running it yk how to fix?

Tap on the blue circled button then you will see the terminal

Nice

Nice

thnx :)