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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))
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