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))

cool

nice....it works

Hi, nice work, but there is a part of code you should pay attention to: lines 48..52.
One can safely assume for torus, that if (x, y) [phi1,theta1] = (x,y)[phi2, theta2], then only one of corresponding luminosities will be positive

But you are working with more complex surfaces like Mobius stripe, you may get following:

output[[2,2], [8,8]] = [10, 3] #I've simplified line 52

as you can see, you will get both wrong output and zbuffer values for x=2, y=8

still wonder, if it is still possible to fill values w/o two cycles for phi and theta

nice

nice

thanks

it's not working for me, something about no module named numpy

it's not working for me, something about no module named numpy

Try pip install numpy in your terminal

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

cool man.....it works

nice

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

It works for me but not the way i wanted IDK why

Really cool!

Putting a sleep of 0.05s at for loop make it perfect.

it's fun, but recommend you need to install pip numpy first .

Uploading 2021-10-14 20-33-50_Trim.mp4…

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?

Awesome!

nice!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

cool!

Really cool!

Putting a sleep of 0.05s at for loop make it perfect.

what line bro?

Umm, I have took this code and copied it to one of my projects
don't worry I gave credit
Just want your permission
btw this is the link to my project
https://github.com/RathoreAgastya/terminal-in-python

Really cool!
Putting a sleep of 0.05s at for loop make it perfect.

what line bro?

did you understood ?
you can import time
then add this line time.sleep(0.08)
at the top of the line 22

it's not working for me, something about no module named numpy

just download it:
pip install numpy

My donut won't stay in place and spin, it just creates new frames under itself :( I'm using pycharm

nice

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

@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