File:Gaussian curvature.svg
Size of this PNG preview of this SVG file: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels.
Original file (SVG file, nominally 600 × 600 pixels, file size: 233 KB)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
| Description |
English: From left to right: a surface of negative Gaussian curvature (hyperboloid), a surface of zero Gaussian curvature (cylinder), and a surface of positive Gaussian curvature (sphere).
Español: De izquierda a derecha: una superficie con curvatura gaussiana negativa (hiperboloide), una superficie con curvatura gaussiana cero (cilindro), y una superficie con curvatura gaussiana positiva (esfera). |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| SVG development |  This trigonometry was created with Matplotlib. |
Creation
This file was created with Python, SciPy, NumPy and Matplotlib. It was later modified using Inkscape.
from __future__ import division
import numpy as np
from numpy import pi, cos, sin, sqrt, outer, ones
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
u = np.linspace(0, 2 * pi, 100)
v = np.linspace(0, pi, 100)
one_v = ones(100)
# Sphere
x1 = 10 * outer(cos(u), sin(v))
y1 = 10 * outer(sin(u), sin(v)) + 17
z1 = 10 * outer(one_v, np.cos(v))
ax.plot_surface(x1, y1, z1, rstride=5, cstride=5, cmap='Spectral',
linewidth=0.5)
# Cylinder
x2 = 6 * outer(cos(u), one_v)
y2 = 6 * outer(sin(u), one_v)
z2 = 20 * outer(one_v, v/pi - 0.5)
ax.plot_surface(x2, y2, z2, rstride=5, cstride=5, cmap='Spectral',
linewidth=0.5)
# Hyperboloid
v = 2*v/pi - 1
x3 = 6 * outer(cos(u), sqrt(1 + v**2))
y3 = 6 * outer(sin(u), sqrt(1 + v**2)) - 16
z3 = 12 * outer(one_v, v)
ax.plot_surface(x3, y3, z3, rstride=5, cstride=5, cmap='Spectral',
linewidth=0.5)
# Fix aspect ratio and axes details
ax.set_xlim(-13, 13)
ax.set_ylim(-13, 13)
ax.set_zlim(-13, 13)
ax.view_init(elev=35, azim=-45)
plt.axis('off')
plt.savefig('Gaussian curvature.svg', transparent=True)
plt.show()
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:11, 28 July 2020 | | 600 × 600 (233 KB) | wikimediacommons>Mrmw | optimized |
File usage
The following 2 pages use this file:
