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As an example, we\ncompute a discretization of a snail curve in polar coordinates\n\n" }, { "__type": "Code", "__tag": 4050, "value": "phi = np.linspace(0, 2.*np.pi, 40)\nr = 0.3 + np.cos(phi)\nx, y = r*np.cos(phi), r*np.sin(phi) # convert to Cartesian coordinates\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nBuild an interpolating curve, parameterizing it by the angle\n\n" }, { "__type": "Code", "__tag": 4050, "value": "spl = make_interp_spline(phi, np.c_[x, y])\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nEvaluate the interpolant on a finer grid (note that we transpose the result\nto unpack it into a pair of x- and y-arrays)\n\n" }, { "__type": "Code", "__tag": 4050, "value": "phi_new = np.linspace(0, 2.*np.pi, 100)\nx_new, y_new = spl(phi_new).T\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nPlot the result\n\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.plot(x, y, 'o')\nplt.plot(x_new, y_new, '-')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-07fa8cc5005b541d.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nBuild a B-spline curve with 2 dimensional y\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x = np.linspace(0, 2*np.pi, 10)\ny = np.array([np.sin(x), np.cos(x)])\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nPeriodic condition is satisfied because y coordinates of points on the ends\nare equivalent\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ax = plt.axes(projection='3d')\nxx = np.linspace(0, 2*np.pi, 100)\nbspl = make_interp_spline(x, y, k=5, bc_type='periodic', axis=1)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, 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