Python Chebyshev Spiral

cheb_spiral.py

"""
Fancy Chebyshev Spiral plotter.

The original idea comes from [Wolfram MathWorld]
(https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html)

This is my Python implementation of the original
plot by Trott 1999, pp. 10 and 84.
"""
import numpy as np
from numpy.polynomial import chebyshev
import matplotlib.pyplot as plt

# Define variables

theta = np.linspace(0, 2 * np.pi, num=1000)
degrees = np.arange(0, 40, 2)

# Define Chebyshev polar function (numpy's wrapper)


def cheby(ths, degs):
    """Polar Chebyshev function"""
    coeffs = degs * [0] + [1]
    xval = ths / np.pi - 1
    return chebyshev.chebval(xval, coeffs) + degs


# Generate values of the polar Chebyshev polynomials

chebspol = []
for th in theta:
    thcheb = []
    for dg in degrees:
        thcheb.append(cheby(th, dg))
    chebspol.append(thcheb)

CHEBSPOL = np.array(chebspol).T

# Plot Chebyshev spiral

fig = plt.figure()

ax1 = plt.subplot(121, projection='polar')
ax2 = plt.subplot(122, projection='polar')


ax1.grid(False)
ax1.set_yticklabels([])
ax1.set_thetagrids([])
ax1.spines['polar'].set_visible(False)

ax2.grid(False)
ax2.set_yticklabels([])
ax2.set_thetagrids([])
ax2.spines['polar'].set_visible(False)

for cpol in CHEBSPOL:
    ax1.plot(theta, cpol)

for pla, plb in CHEBSPOL.reshape(-1, 2, 1000):
    ax2.fill_between(theta, pla, plb, facecolor='black')

plt.show()

cspiral.md

Polar Chebyshev Spiral in Python

lisence

MIT License

Copyright (c) 2020 Ramon L. PANADES-BARRUETA

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