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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from functools import cache | |
| def normalize_vecs(vecs): | |
| return vecs / np.linalg.norm(vecs, axis=1)[:, np.newaxis] | |
| @cache | |
| def generate_vectors_structured(num_samples): | |
| """Generates vectors around the sphere, at regular intervals.""" | |
| # Uses the Fibonnaci lattice to generate evenly distributed points on a sphere | |
| # https://arxiv.org/pdf/0912.4540.pdf | |
| # https://extremelearning.com.au/how-to-evenly-distribute-points-on-a-sphere-more-effectively-than-the-canonical-fibonacci-lattice/ | |
| golden_ratio = (1 + 5 ** 0.5) / 2.0 | |
| i = np.arange(0, num_samples) | |
| theta = np.arccos(1 - (2 * (i + 0.5)) / num_samples) | |
| phi = 2 * np.pi * i / golden_ratio | |
| vectors = np.empty((num_samples, 3)) | |
| vectors[:, 0] = np.sin(theta) * np.cos(phi) | |
| vectors[:, 1] = np.cos(theta) | |
| vectors[:, 2] = np.sin(theta) * np.sin(phi) | |
| return vectors | |
| @cache | |
| def generate_vectors_pr(num_samples_per_axis): | |
| X = np.linspace(-1.0, 1.0, num=num_samples_per_axis) | |
| Y = np.linspace(-1.0, 1.0, num=num_samples_per_axis) | |
| Z = np.linspace(-1.0, 1.0, num=num_samples_per_axis) | |
| XX, YY, ZZ = np.meshgrid(X, Y, Z) | |
| vectors = np.vstack([XX.ravel(), YY.ravel(), ZZ.ravel()]).T | |
| return normalize_vecs(vectors) | |
| def plot_vectors(vectors): | |
| """Display a list of 3D vectors in a plot.""" | |
| fig = plt.figure() | |
| ax = fig.add_subplot(111, projection="3d") | |
| ax.quiver([0], [0], [0], [3], [0], [0]).set_color("red") # main axes | |
| ax.quiver([0], [0], [0], [0], [3], [0]).set_color("green") | |
| ax.quiver([0], [0], [0], [0], [0], [3]).set_color("blue") | |
| X = Y = Z = np.zeros(len(vectors)) | |
| U, V, W = zip(*(vectors)) | |
| ax.quiver(X, Y, Z, U, V, W) | |
| ax.set_xlim([-1.5, 1.5]) | |
| ax.set_ylim([-1.5, 1.5]) | |
| ax.set_zlim([-1.5, 1.5]) | |
| ax.set_box_aspect([1.0, 1.0, 1.0]) | |
| plt.show() | |
| def main(): | |
| n = 5 | |
| vectors = generate_vectors_pr(n) | |
| plot_vectors(vectors) | |
| vectors = generate_vectors_structured(n*n*n) | |
| plot_vectors(vectors) | |
| if __name__ == "__main__": | |
| main() |
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