File:Constant gaussian curvature.svg
Summary
| Description |
English: Surfaces with constant Gaussian curvature. From left to right: a surface of negative Gaussian curvature, a surface of zero Gaussian curvature (cylinder), and a surface of positive Gaussian curvature (sphere). The surface of negative curvature given by
Español: Superficies de curvatura gaussiana constante. De izquierda a derecha: una superficie con curvatura gaussiana negativa, una superficie con curvatura gaussiana cero (cilindro), y una superficie con curvatura gaussiana positiva (esfera). La superficie de curvatura negativa está dada por
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| Date | |
| Source | Own work |
| Author | Nicoguaro |
| SVG development | |
| Source code | Python code"""
Examples of surfaces with constant Gaussian curvature.
Created with Matplotlib 3.4.3.
"""
import numpy as np
from numpy import pi, cos, sin, sqrt, outer, ones, sinh, cosh
from scipy.integrate import quad
import matplotlib.pyplot as plt
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, cos(v))
ax.plot_surface(x1, y1, z1, rstride=5, cstride=5, cmap='Spectral',
linewidth=0.5, edgecolors="#3c3c3c")
# 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, edgecolors="#3c3c3c")
# Negative Gaussian curvature
u = np.linspace(-pi, pi, 100)
v = np.linspace(-1.4436, 1.4436, 100)
aux = np.zeros_like(v)
for cont, val in enumerate(v):
aux[cont] = quad(lambda t: sqrt(1 - 0.25*sinh(t)**2), 0, val)[0]
x3 = 4 * outer(cos(u), cosh(v))
y3 = 4 * outer(sin(u), cosh(v)) - 16
z3 = 8 * outer(one_v, aux)
ax.plot_surface(x3, y3, z3, rstride=5, cstride=5, cmap='Spectral',
linewidth=0.5, edgecolors="#3c3c3c")
# Fix aspect ratio and axes details
ax.set_box_aspect((np.ptp(np.column_stack((x1, x2, x3))),
np.ptp(np.column_stack((y1, y2, y3))),
np.ptp(np.column_stack((z1, z2, z3)))))
ax.view_init(elev=35, azim=-45)
plt.axis('off')
plt.savefig('Constant gaussian curvature.svg', transparent=True)
plt.show()
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