File:Torus cycles.svg

Original file(SVG file, nominally 512 × 780 pixels, file size: 46 KB)

Summary

Description
English: Homology cycles on a torus. Radius of magenta circle is and radius of red circle is . Image created in python and subsequently cropped and rotated manually using a text editor.
Date
Source Own work
Author Krishnavedala
Other versions

Torus cycles2.svg

SVG development
Created with Matplotlib-logo.svg
This vector image was created with Matplotlib.

Python

from mpl_toolkits.mplot3d import axes3d
from matplotlib.patches import Circle
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d.art3d as art3d
import numpy as np

R, r = 15, 5

def get_x(phi, theta):
    global r, R
    return (R + r * np.cos(phi)) * np.cos(theta)

def get_y(phi, theta):
    global r, R
    return (R + r * np.cos(phi)) * np.sin(theta)

def get_z(phi, theta):
    global r
    return r * np.sin(phi)

if __name__ == "__main__":
    fig = plt.figure(figsize=(10,10))
    ax = fig.add_subplot(111, projection='3d')

    ph = th = np.linspace (-np.pi, np.pi,30)
    phi, theta = np.meshgrid (ph, th)

    x = np.array([get_x(p,t) for p,t in zip(np.ravel(phi), np.ravel(theta))])
    X = x.reshape(phi.shape)
    y = np.array([get_y(p,t) for p,t in zip(np.ravel(phi), np.ravel(theta))])
    Y = y.reshape(phi.shape)
    z = np.array([get_z(p,t) for p,t in zip(np.ravel(phi), np.ravel(theta))])
    Z = z.reshape(phi.shape)
    C1 = Circle( (R,0), radius=r, fc='none', ec='red')
    C2 = Circle( (0,0), radius=R, fc='none', ec='magenta')

    ax.plot_wireframe(X, Y, Z, color='#CCCCCC')
    ax.add_patch(C1)
    ax.add_patch(C2)
    art3d.pathpatch_2d_to_3d(C1, z=0, zdir='y')
    art3d.pathpatch_2d_to_3d(C2, z=r, zdir='z')

    ax.set_xlim3d(-20,20)
    ax.set_ylim3d(-20,20)
    ax.set_zlim3d(-20,20)
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')
    ax.set_axis_off()

    ax.view_init(elev=30, azim=-45)
    plt.show()
    plt.savefig('torus.svg', bbox_inches='tight', pad_inches=.15, \
        bbox_extra_artists=[C1,C2], transparent='true')

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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 his or her 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/TimeThumbnailDimensionsUserComment
current16:38, 14 April 2014Thumbnail for version as of 16:38, 14 April 2014512 × 780 (46 KB)Krishnavedala
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):

Global file usage

The following other wikis use this file:

Metadata