File:Unduloid.svg
Summary
| Description |
English: Plot of the unduloid constant mean curvature surface, generated by rotating an elliptic catenary around the x-axis.
Español: Gráfico del unduloide. Esta superficie tiene curvature media constante y es generada a partir de rotar una catenaria elíptica alrededor del eje x.
Türkçe: Sabit ortalama egri yuzeyli unduloid grafigi. Eliptik bir zincir egrisinin x ekseni etrafinda dondurulmesiyle elde edilmistir. |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| Creation | The parameterization used was
where and are parameters. For the plot and . This file was created with Python,NumPy and Matplotlib. |
| SVG development | |
| Source code | Python codefrom __future__ import division
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import quad
def fun(alpha, a, b):
return np.sqrt(a**2*np.sin(alpha)**2 + b**np.cos(alpha)**2)
a = 1.7
b = 1.2
u = np.linspace(0, 20, 100)
v = np.linspace(0, 2*np.pi, 30)
integral = np.array([quad(fun, 0, uval, args=(a, b))
for uval in u])
xu = integral[:, 0]
xu = xu + np.sqrt(a**2 - b**2)*np.sin(u)*(np.sqrt(a**2 - b**2)*np.cos(u) + a)/\
fun(u, a, b)
yu = b*(np.sqrt(a**2 - b**2)*np.cos(u) + a)/fun(u, a, b)
x = np.outer(xu, np.ones_like(v))
y = np.outer(yu, np.cos(v))
z = np.outer(yu, np.sin(v))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap="summer", alpha=0.6,
lw=0.4)
ax.view_init(azim=-60, elev=30)
ax.set_xlim([0, 35])
ax.set_ylim([-10, 10])
ax.set_zlim([-10, 10])
plt.savefig("Unduloid.svg", bbox_inches="tight", transparent=True)
plt.show()
|
![{\displaystyle y=b\left[{\frac {{\sqrt {a^{2}-b^{2}}}\cos u+a}{\sqrt {a^{2}\sin ^{2}u+b^{2}\cos ^{2}u}}}\right]\cos v}](https://wikimedia.org/api/rest_v1/media/math/render/svg/651bd25bf71aea99470997681e549fabcb30296d)
![{\displaystyle z=b\left[{\frac {{\sqrt {a^{2}-b^{2}}}\cos u+a}{\sqrt {a^{2}\sin ^{2}u+b^{2}\cos ^{2}u}}}\right]\sin v}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3bd3155cbd619e028867e41e258938146e0b0932)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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