Cornu’s Spiral

Cornu’s spiral is the curve parameterized by: Where C and S are the Fresnel functions, sometimes called the Fresnel cosine integral and Fresnel sine integral. Here’s a plot of the spiral. Both Fresnel functions approach ½ as t → ∞ and so the curve slowly spirals toward (½, ½) in the first quadrant. And by symmetry, because both functions are odd, the curve spirals toward (-½, -½) in the third quadrant. Here’s the Python code used to make the plot: from scipy.special import fresnel from scipy import linspace import matplotlib.pyplot as plt t = linspace(-7, 7, 1000) y, x = fresnel(t) plt.plot(x, y) plt.axes().set_aspect(“equal”) plt.show() The SciPy function fresnel returns both Fresnel functions at the same time. It returns them in the order (S, C) so the code reverses the order…


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