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), " ")
zbuffer = np.zeros((screen_size, screen_size))
cos_phi = np.cos(phi := np.arange(0, 2 * np.pi, phi_spacing))
sin_phi = np.sin(phi)
cos_theta = np.cos(theta := np.arange(0, 2 * np.pi, theta_spacing))
sin_theta = np.sin(theta)
circle_x = R2 + R1 * cos_theta
circle_y = R1 * sin_theta
x = (np.outer(cos_B * cos_phi + sin_A * sin_B * sin_phi, circle_x) - circle_y * cos_A * sin_B).T
y = (np.outer(sin_B * cos_phi - sin_A * cos_B * sin_phi, circle_x) + circle_y * cos_A * cos_B).T
z = ((K2 + cos_A * np.outer(sin_phi, circle_x)) + circle_y * sin_A).T
ooz = np.reciprocal(z)
xp = (screen_size / 2 + K1 * ooz * x).astype(int)
yp = (screen_size / 2 - K1 * ooz * y).astype(int)
L1 = (((np.outer(cos_phi, cos_theta) * sin_B) - cos_A * np.outer(sin_phi, cos_theta)) - sin_A * sin_theta)
L2 = cos_B * (cos_A * sin_theta - np.outer(sin_phi, cos_theta * sin_A))
L = np.around(((L1 + L2) * 8)).astype(int).T
mask_L = L >= 0
chars = illumination[L]
for i in range(90):
mask = mask_L[i] & (ooz[i] > zbuffer[xp[i], yp[i]])
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))