I am looking for a pythonic solution of
https://en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas
A solution with Julia is available at
https://github.com/federicomor/frenet-trihedron
Hi!
This is roughly the translation of the above Julia code to Python:
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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from datetime import datetime
# Define the curve parameters
n = 200
t = np.linspace(0, 6 * np.pi, n)
def f(t):
return t * np.cos(t)
def g(t):
return t * np.sin(t)
def h(t):
return t
def f1(t):
return np.cos(t) - t * np.sin(t)
def f2(t):
return -2 * np.sin(t) - t * np.cos(t)
def g1(t):
return np.sin(t) + t * np.cos(t)
def g2(t):
return 2 * np.cos(t) - t * np.sin(t)
def h1(t):
return 1
def h2(t):
return 0
x = f(t)
y = g(t)
z = h(t)
# Graphical Parameters
molt = 3.0
limx = [np.min(x) - 1, np.max(x) + 1]
limy = [np.min(y) - 1, np.max(y) + 1]
limz = [np.min(z) - 1, np.max(z) + 2]
cam_height = 30
cam_angle = np.linspace(0, 90, num=len(t))
# Create the animation
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
def update(i):
ax.clear()
ax.plot(x, y, z, label="Curve")
draw_trihedron(ax, t[i], i, molt)
ax.set_xlim(limx)
ax.set_ylim(limy)
ax.set_zlim(limz)
ax.view_init(elev=cam_angle[i], azim=0)
print(f"{int(100 * i / len(t))}% -> ")
def draw_trihedron(ax, t, i, molt):
trihedron_size = molt
trihedron = np.array([[0, 0, 0],
[trihedron_size, 0, 0],
[0, trihedron_size, 0],
[0, 0, trihedron_size]])
R = np.array([[f1(t), g1(t), h1(t)],
[f2(t), g2(t), h2(t)],
[0, 0, 1]])
trihedron_rotated = trihedron.dot(R.T)
ax.plot(trihedron_rotated[:, 0], trihedron_rotated[:, 1], trihedron_rotated[:, 2], color='r')
ani = FuncAnimation(fig, update, frames=len(t), interval=100)
plt.show()
# Save the animation as a GIF
now = datetime.now().strftime("%Y-%m-%d_%H:%M:%S")
ani.save(f"{now}.gif", writer='imagemagick', fps=15)
print("END!")
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You need to install numpy and matplotlib to run the above code:
pip install matplotlib numpy
Also you may need imagemagick or ffmpeg:
sudo apt-get install imagemagick
sudo apt-get install ffmpeg
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