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@cesarkawakami
Created March 20, 2017 01:30
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{"nbformat_minor": 2, "cells": [{"source": "# Playing with Ellipses\n\n$$\n \\newcommand{\\vect}[1]{\\mathbf{#1}}\n \\newcommand{\\hypot}[2]{\\sqrt{#1^2 + #2^2}}\n$$\n\nAn ellipsis centered at the origin can be parameterized as\n$$\n \\vect{p} = \\vect{a} \\sin\\theta + \\vect{b} \\cos\\theta\n$$\nWhere $\\vect{a}$ and $\\vect{b}$ are orthogonal to each other.\n\nThus, on the $y$ axis,\n\\begin{align\\*}\n p_y &= a_y \\sin\\theta + b_y \\cos\\theta \\\\\\\\\n &= \\hypot{a_y}{b_y} \\Biggl( \n \\frac{a_y}{\\hypot{a_y}{b_y}} \\sin\\theta + \\frac{b_y}{\\hypot{a_y}{b_y}} \\cos\\theta\n \\Biggr)\n\\end{align\\*}\n\nPicking $\\alpha$ such that $\\displaystyle \\cos\\alpha = \\frac{a_y}{\\hypot{a_y}{b_y}}$ we then have\n\\begin{align\\*}\n p_y &= \\hypot{a_y}{b_y} ( \\cos\\alpha \\sin\\theta + \\sin\\alpha \\cos\\theta ) \\\\\\\\\n &= \\hypot{a_y}{b_y} \\sin(\\alpha + \\theta)\n\\end{align\\*}\n\nSolutions for the above are\n$$\n \\theta = \\arcsin\\Biggl( \\frac{p_y}{\\hypot{a_y}{b_y}} \\Biggr) - \\alpha + 2k\\pi\n \\quad \\text{for $k$ in $\\mathbb{Z}$}\n$$\nand\n$$\n \\theta = \\pi - \\arcsin\\Biggl( \\frac{p_y}{\\hypot{a_y}{b_y}} \\Biggr) - \\alpha + 2k\\pi \n \\quad \\text{for $k$ in $\\mathbb{Z}$}\n$$", "cell_type": "markdown", "metadata": {}}, {"execution_count": 78, "cell_type": "code", "source": "%pylab inline\nimport ipywidgets\nfigsize(10, 6)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "Populating the interactive namespace from numpy and matplotlib\n"}], "metadata": {"collapsed": false}}, {"execution_count": 58, "cell_type": "code", "source": "# double ay = a.y;\n# double by = b.y;\n\n# if ((ay*ay + by*by) < 0.0) {\n# return {0.0, 0.0};\n# }\n\n# double alpha = acos(ay / sqrt(ay*ay + by*by));\n# double theta = asin((y-circle_center.y)/sqrt(ay*ay + by*by));\n# double theta1 = theta - alpha;\n# double theta2 = M_PI - theta - alpha;\n\n# double z1 = circle_center.z + radius*(sin(theta1)*a.z + cos(theta1)*b.z);\n# double z2 = circle_center.z + radius*(sin(theta2)*a.z + cos(theta2)*b.z);\n \ndef find_z(ay, by, cy, y, az, bz, cz):\n alpha = arccos(ay / sqrt(ay*ay + by*by))\n theta = arcsin( (y - cy) / sqrt(ay*ay + by*by) )\n theta1 = theta - alpha\n theta2 = pi - theta - alpha\n \n z1 = cz + az*sin(theta1) + bz*cos(theta1)\n z2 = cz + az*sin(theta2) + bz*cos(theta2)\n return z1, z2\n", "outputs": [], "metadata": {"collapsed": true}}, {"execution_count": 80, "cell_type": "code", "source": "def rotation_matrix(axis, theta):\n \"\"\"\n Return the rotation matrix associated with counterclockwise rotation about\n the given axis by theta radians.\n \"\"\"\n axis = asarray(axis)\n axis = axis/sqrt(dot(axis, axis))\n a = cos(theta/2.0)\n b, c, d = -axis*sin(theta/2.0)\n aa, bb, cc, dd = a*a, b*b, c*c, d*d\n bc, ad, ac, ab, bd, cd = b*c, a*d, a*c, a*b, b*d, c*d\n return np.array([[aa+bb-cc-dd, 2*(bc+ad), 2*(bd-ac)],\n [2*(bc-ad), aa+cc-bb-dd, 2*(cd+ab)],\n [2*(bd+ac), 2*(cd-ab), aa+dd-bb-cc]])\n\ndef euler_rotate(rx, ry, rz):\n return rotation_matrix([1, 0, 0], rx) @ rotation_matrix([0, 1, 0], ry) @ rotation_matrix([0, 0, 1], rz)", "outputs": [], "metadata": {"collapsed": true}}, {"execution_count": 83, "cell_type": "code", "source": "rx, ry, rz, rd = .11, .11, .11, 3.14\n\[email protected](rx=(0, 2*pi, 0.01),\n ry=(0, 2*pi, 0.01), \n rz=(0, 2*pi, 0.01))\ndef go(rx=.52, ry=.84, rz=.28):\n ax, ay, az = [0, 3, 0] @ euler_rotate(rx, ry, rz)\n bx, by, bz = [0, 0, 6] @ euler_rotate(rx, ry, rz)\n cx, cy, cz = 0, -10, 10\n\n theta = arange(0, 2*pi, 0.001)\n y = cy + ay*sin(theta) + by*cos(theta)\n z = cz + az*sin(theta) + bz*cos(theta)\n plot(y, z, 'r')\n title('parameterized ellipsis')\n show()\n\n y = linspace(min(y), max(y), 10000)\n zb = find_z(ay, by, cy, y, az, bz, cz)[0]\n ze = find_z(ay, by, cy, y, az, bz, cz)[1]\n plot(y, zb, 'r', y, ze, 'g')\n title('find_z for each y')\n show()", "outputs": [{"output_type": "display_data", "data": {"image/png": 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iVyMVTIvSJTuMHQstW8LNN3vjTq1REJGYiorgjDNgu+2ga9fY1ch60KJ0yV2D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\nERGRJClQiYiIiCQpqUBlZpub2Ztm9rW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SRlSoJLicOgVt20K2bLBgAeTI4TqRiISwXSd20WVSF75p+w3Fcxd3HUfSkCal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\nSK4suVxHknT0e9zvROyM4LvN3zFt2zS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