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))

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 :)

im so happy

using os library.It better

like this:

import numpy as np
from time import sleep
import os

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")
os.system('cls')
pprint(render_frame(A, B))
sleep(0.05)