File:KleinBottle-cut.svg
Size of this PNG preview of this SVG file: 217 × 465 pixels. Other resolutions: 112 × 240 pixels | 224 × 480 pixels | 358 × 768 pixels | 478 × 1,024 pixels | 955 × 2,048 pixels.
Original file (SVG file, nominally 217 × 465 pixels, file size: 109 KB)
Summary
| Description |
English: Cut-away version of an immersion of a Klein bottle into . |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| 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 numpy import pi, linspace, cos, sin
def x_(u, v):
x = -2 + 2*cos(v) - cos(u)
x[v<3*pi] = -2 + (2 + cos(u[v<3*pi]))*cos(v[v<3*pi])
x[v<2*pi] = cos(u[v<2*pi])*(2.5 - 1.5*cos(v[v<2*pi]))
return x
def y_(u, v):
y = sin(u)
y[v<2*pi] = sin(u[v<2*pi])*(2.5 - 1.5*cos(v[v<2*pi]))
return y
def z_(u, v):
z = -3*v + 12*pi
z[v<3*pi] = (2 + cos(u[v<3*pi]))*sin(v[v<3*pi]) + 3*pi
z[v<2*pi] = 3*v[v<2*pi] - 3*pi
z[v<pi] = -2.5*sin(v[v<pi])
return z
u = linspace(pi, 2*pi, 10)
v = linspace(0, 4*pi, 38)
u, v = np.meshgrid(u, v)
x = x_(u, v)
y = y_(u, v)
z = -z_(u, v)
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap="YlGnBu_r", alpha=0.8,
lw=1)
ax.set_xlim(-5, 5)
ax.set_ylim(-5, 5)
ax.set_zlim(-9, 1)
ax.view_init(azim=130, elev=30)
plt.axis("off")
plt.savefig("KleinBottle-cut.svg", bbox_inches="tight", transparent=True)
plt.show()
|
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 | 02:13, 18 February 2016 | | 217 × 465 (109 KB) | wikimediacommons>Nicoguaro | User created page with UploadWizard |
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