161:""" f: the function that produces the curve df: the derivative. That is, df(x) = f'(x) x0: the origin point l0: the string length at origin point dxs: the differential points at which to plot the involute. Assumed to be sorted in increasing order returns f_xs, f_ys, inv_xs, inv_ys """ f_xs = x0 + dxs f_ys = f(f_xs) inv_xs = np.zeros(len(dxs)) inv_ys = np.zeros(len(dxs)) arclength_integrand = lambda x: np.sqrt(1 + df(x)**2) for i in range(len(dxs)): x = x0 + dxs arclength = quad(arclength_integrand, x0, x) string_length = l0 - arclength string_angle = np.arctan(df(x)) inv_xs = f_xs + string_length * np.cos(string_angle) inv_ys = f_ys + string_length * np.sin(string_angle) return f_xs, f_ys, inv_xs, inv_ys
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xlim_low = -0.5 xlim_width = 2 ylim_low = -0.5 plt.xlim(xlim_low, xlim_low + xlim_width) plt.ylim(ylim_low, ylim_low + xlim_width * y_x_ratio) plt.savefig("involutes of a cubic curve.svg") plt.show()
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f_xs, f_ys, inv_xs, inv_ys = involute(f, df, 0, l0=0.8, dxs=np.arange(200) / 100 - 1) y_x_ratio = 1 plt.figure(figsize=(16, int(16*y_x_ratio))) plt.plot(f_xs, f_ys) for l0 in np.arange(20)/10-1:
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import numpy as np import matplotlib.pyplot as plt from scipy.integrate import quad # numerical integration import matplotlib.cm as cm # for colormaps
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f_xs, f_ys, inv_xs, inv_ys = involute(f, df, 0, l0=l0, dxs=np.arange(200) / 100 - 0.5) plt.plot(inv_xs, inv_ys, color='green', linewidth=0.2)
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y = f(x) slope = df(x) plot_line(x, y, slope, -1, +2, color=cm.viridis(x), marker='o',markersize=5, linewidth=1)
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693:Evolventti
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613:Dimensions
389:some value
153:```python
27:File usage
610:Thumbnail
607:Date/Time
565:inception
226:Licensing
150:English:
701:Metadata
665:Involute
333:Captions
278:to remix
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639:(59 KB)
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187:```
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
