File:Unduloid.svg
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Original file (SVG file, nominally 575 × 449 pixels, file size: 773 KB)
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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 |  This plot was created with Matplotlib. |
| 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:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:47, 16 February 2016 | | 575 × 449 (773 KB) | Nicoguaro | User created page with UploadWizard |
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