File:Nodary.svg

Original file (SVG file, nominally 450 × 270 pixels, file size: 22 KB)

Summary

Description
English: Plot of the nodary curve, the roulette of a hyperbola along the x-axis.
Date
Source Own work
Author Nicoguaro

Creation

The parameterization used was

with where and are parameters.


This file was created with Python,NumPy and Matplotlib.

from __future__ import division
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import quad

plt.rcParams["axes.spines.top"] = False
plt.rcParams["axes.spines.right"] = False


def fun(alpha, beta):
    return np.sin(alpha)**2/np.sqrt(np.sin(alpha)**2 + beta)    
    
a = 1.
b = 0.8
beta = a**2/b**2
u = np.linspace(0, 9*np.pi, 500)
integral = np.array([quad(fun, 0, uval, args=(beta,))
					for uval in u])
x = integral[:, 0]
x = a*(1 - np.cos(u) + x)
y = a*(np.sin(u) + np.sqrt(np.sin(u)**2 + beta))
plt.figure(figsize=(5, 3))
plt.plot(x, y, lw=2)
plt.ylim([0, 3.0])
plt.savefig("Nodary.svg", transparent=True)
plt.show()

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
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.

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depicts

14 February 2016

File history

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Date/TimeThumbnailDimensionsUserComment
current17:04, 12 April 2018Thumbnail for version as of 17:04, 12 April 2018450 × 270 (22 KB)NicoguaroRemove parts of the curve outside.
02:29, 15 February 2016Thumbnail for version as of 02:29, 15 February 2016900 × 450 (23 KB)NicoguaroRemove background
02:16, 15 February 2016Thumbnail for version as of 02:16, 15 February 2016741 × 404 (23 KB)NicoguaroUser created page with UploadWizard

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