Splined_epitrochoid.svg


Summary

This diagram was created with SageMath .
Description

Made with Sage; code is as follows:

# Five-petaled epitrochoid via splining the points:
# Draw an epitrochoid, fixed circle radius R, rotating circle
# of radius r, pen at distance d from center of rotating circle.

R = 5
r = 2
d = 3
rotations = ((R + r) / r).denom()
v = []
step = 0.2
for t in srange(0, 2 * pi * rotations, step):
    v.append(((R + r) * cos(t) - d * cos(((R + r) / r) * t),
             (R + r) * sin(t) - d * sin(((R + r) / r) * t)))
x_spline = spline([(RDF(i) / len(v), v[i][0]) for i in range(len(v))] + [(1, v[0][0])])
y_spline = spline([(RDF(i) / len(v), v[i][1]) for i in range(len(v))] + [(1, v[0][1])])
show(points(v, rgbcolor=(1, 0, 0), pointsize=10) + parametric_plot((x_spline, y_spline), (x, 0, 1), thickness=0.5),
                                                                   figsize=[4, 4], ticks=[2.5, 2.5], xmin=-10)
Date (UTC)
Source This file was derived from: Splined epitrochoid.png :
Author


This is a retouched picture , which means that it has been digitally altered from its original version. Modifications: Vectorized . The original can be viewed here: Splined epitrochoid.png : .

Licensing

This work has been released into the public domain by its author, dino , at the English Wikipedia project . This applies worldwide.

In case this is not legally possible:
dino grants anyone the right to use this work for any purpose , without any conditions, unless such conditions are required by law.

Original upload log

This image is a derivative work of the following images:

  • File:Splined_epitrochoid.png licensed with PD-user-w
    • 2010-07-25T20:52:50Z Aleksd 400x400 (27936 Bytes) {{Information |Description=made with SAGE; code follows: # Five-petaled epitrochoid via splining the points: # Draw an epitrochoid, fixed circle radius R, rotating circle # of radius r, pen at distance d from center of rota

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29 January 2012