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@nmayorov
Created August 5, 2018 17:32
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RotationSpline test
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{
"cells": [
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.spatial.transform import RotationSpline, Rotation"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"angles = np.array([\n",
" [-10, 20, 30],\n",
" [0, 15, 40],\n",
" [-30, 45, 30],\n",
" [20, 45, 90]\n",
"])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"times = [0, 10, 20, 30]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"r = Rotation.from_euler('xyz', angles, degrees=True)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"spline = RotationSpline(times, r)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ts = np.linspace(times[0], times[-1], 100)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"angles_s = spline(ts, 0).as_euler('xyz', degrees=True)\n",
"omega_s = np.rad2deg(spline(ts, 1))\n",
"alpha_s = np.rad2deg(spline(ts, 2))"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"omega = np.rad2deg(spline(times, 1))\n",
"alpha = np.rad2deg(spline(times, 2))"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11b962198>,\n",
" <matplotlib.lines.Line2D at 0x11b93c710>,\n",
" <matplotlib.lines.Line2D at 0x11bb384a8>]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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artuktmMqqiIiIuIxKuoqmJs2F4DbB91Ot9Bu1gYSS6moioiIiMd4dcurFFQXEB8czx2D\n7rA6jlhMRVVEREQ8wq6iXby35z0ApidN15qpoqIqIiIi1nO6nMxaPwuX4eLybpczNm6s1ZHEA6io\nioiIiOX+b///sb1wO0HeQTyc+LDVccRDqKiKiIiIpUprS3l508sA3Dv0XiIDIi1OJJ5CRVVEREQs\n9crmVyipLaFnh57c3Pdmq+OIB1FRFREREcvsLtrNv/b9C4DHkx7Hy+5lcSLxJCqqIiIiYokTd6By\nGS6u6HYFidGJVkcSD6OiKiIiIpb45OAnbCnYgr+XPw+OfNDqOOKBVFRFRESkxVXUVfDChhcAuGvw\nXUQHRlucSDyRiqqIiIi0uIVbF1JUU0TXkK78qv+vrI4jHkpFVURERFrUgZIDLN69GIBHRz2Kj8PH\n4kTiqVRURUREpMUYhsGctDk0GA1cFH8R4+PGWx1JPJiKqoiIiLSY1ZmrSc1Jxcfuw7TEaVbHEQ+n\noioiIiItotZZy/PpzwPwm4G/oXNwZ4sTiadTURUREZEW8e6udzlWcYxI/0huH3i71XGkFVBRFRER\nEbfLr8pn0bZFAEwdMZUA7wCLE0lroKIqIiIibvfSppeobqhmcKfBTOk+xeo40kqoqIqIiIhbbS/Y\nzkcHPgLg0cRHsdtUP+Ts6CdFRERE3MZluPhz2p8BuLrH1QzqNMjiRNKaqKiKiIiI23x68FO2FW4j\nwCuAqcOnWh1HWhkVVREREXGLqvoq5m+cD8Cdg++kU0AnixNJa6OiKiIiIm7x+vbXya/OJy4ojl/2\n/6XVcaQVUlEVERGRZpddkc3bO98G4KGRD+Hr8LU4kbRGbi+qWVlZ3HrrrYSHh+Pv78+gQYPYsGFD\n4+OGYTBz5kxiYmLw9/dn8uTJZGRkuDuWiIiIuNH8jfOpc9WRGJ3IpC6TrI4jrZRbi2pxcTHjxo3D\n29ubzz77jF27dvHCCy/QsWPHxufMmzePl19+mYULF5KamkpgYCCXXXYZNTU17owmIiIibrIlfwuf\nHf4MGzamJU7DZrNZHUlaKS93vvjcuXOJj4/nzTffbDyWkJDQ+G/DMJg/fz7Tp0/nmmuuAeCdd94h\nKiqKZcuWcdNNN7kznoiIiDQzl+FibtpcAK7rdR19w/panEhaM7eeUf3oo48YOXIkN9xwA5GRkQwb\nNozXXnut8fFDhw6Rm5vL5MmTG4+FhoaSlJRESkrKaV+ztraWsrKyJpuIiIh4hk8PfsqOoh0EeAXw\n+2G/tzqOtHJuLaoHDx7kb3/7G7169eLzzz/nnnvu4f777+ftt83B1bm5uQBERUU1+byoqKjGx75v\nzpw5hIaGNm7x8fHu/BZERETkLFXVVzF/08nlqCL8IyxOJK2dW4uqy+Vi+PDhzJ49m2HDhnHXXXdx\n5513snDhwvN+zccee4zS0tLGLTMzsxkTi4iIyPl6a+db5FdpOSppPm4tqjExMfTv37/JsX79+nH0\n6FEAoqOjAcjLy2vynLy8vMbHvs/X15eQkJAmm4iIiFgrtzKXN3eYc1IeGPGAlqOSZuHWojpu3Dj2\n7t3b5Ni+ffvo2rUrYE6sio6OZtWqVY2Pl5WVkZqaypgxY9wZTURERJrRS5teosZZw/DI4Vza9VKr\n40gb4dZZ/w888ABjx45l9uzZ3HjjjaSlpbFo0SIWLVoEgM1mY+rUqcyaNYtevXqRkJDAjBkziI2N\n5dprr3VnNBEREWkm2wu288nBTwC0HJU0K7cW1cTERD744AMee+wxnn76aRISEpg/fz633HJL43Om\nTZtGZWUld911FyUlJYwfP57ly5fj5+fnzmgiIiLSDAzDYF76PACu7nE1AyIGWJxI2hKbYRiG1SF+\nirKyMkJDQyktLdV4VRERkRa2/NByHl7zMP5e/nxy3SdEBkRaHUk80Pn2NbffQlVERETaplpnLX/Z\n+BcAbht4m0qqNDsVVRERETkv7+56l+zKbKICovjNgN9YHUfaIBVVEREROWeF1YW8ts282+Qfhv8B\nfy9/ixNJW6SiKiIiIufslc2vUNVQxaCIQUzpPsXqONJGqaiKiIjIOdlzfA8fZHwAmMtR2W2qE+Ie\n+skSERGRs2YYBs+lP4eBweXdLmdo5FCrI0kbpqIqIiIiZ+3LzC9Jy03Dx+7DAyMesDqOtHEqqiIi\nInJW6p31vLjxRQB+NeBXxAbFWpxI2joVVRERETkr7+15jyNlRwj3C+eOQXdYHUfaARVVERER+VHH\na47z961/B8zlqAK9Ay1OJO2BiqqIiIj8qFc3v0p5fTn9wvpxdY+rrY4j7YSKqoiIiPygfcX7+HfG\nvwFzOSqH3WFxImkvVFRFRETkjAzDYF76PFyGi0u6XsLI6JFWR5J2REVVREREzuirzK9IzUnFx+7D\ngyMetDqOtDMqqiIiInJa9c56nt/wPGAuR9U5uLPFiaS98bI6gIiIiHim9/a8x9Hyo+ZyVANvh/pq\nqCmFhhqw2QGb+dH27UffYPAOMPdFmoGKqoiISHvXUAelmVB8GEqOQPFhjh/PYGH1TrDBH/JzCJyb\nAM66H38thw/4h0FA2MmPHbpAWAJ0TDA/hnYBhyqI/Dj9lIiIiLQn9dWQtxOyN0POFsjeCgW7wdXQ\n5GkLwjtSERJMv9o6rinKPfmAzQ4OX8AAwwDDZf7b5TQ/OuugItfczsTmMAtrzJBvt6EQMxj8O7rj\nO5ZWTEVVRESkLaurgqPJcPBrOLQGcreD4Tz1eV7+0LEbdOzGnqCO/Lt4HQDTRj2GPXok+IWam08Q\n2E8zxcUwoK4Sqouh+jhUHTf/XVlgnqk9fgiOHzT/7ayFov3mtmPpydfo2A06J0K38dBtAoR11zCC\ndk5FVUREpC0xDMjZChlfmOX0WNqpl+wDIiB2qHkm88TH0M5gs2EYBnOW/wYDuLzb5Ywc+puz+7o2\nG/gGmVuH+DM/z+WC8hzzLG7O1pNb8eGT2/Z/mc8Njvm2tI6HHpN++HWlTVJRFRERae1cLjiWDrs/\nMreSo00fD+kM3S+E7hdA17EQEnfGM5XLDy9nU/4m/Bx+/HHkH5s/q90OoXHm1nPyyePVxZC9BY6u\nh8PrzIJdnmOW1hPFNWog9L4Mel0GnUeCbjzQ5qmoioiItEaGAVkbYes/YPfHTceEevlDz0nQ42Kz\noJ7lJfSq+ipe2PACALcPup3owGj3ZD8d/47Q4yJzA3Ms7bENZmk9+JVZXPN2mNvaF8yJWr0vg/7X\nmN+nl2/LZZUWYzMMw7A6xE9RVlZGaGgopaWlhISEWB1HRETEvcpyYNs/Yct7ULj35HHfEOh9OfS7\nyjxT6RNwzi+9YPMC/r7t78QFxbHsmmX4efk1Y/CfqOo47F8J+5abH2tKTz7mGwJ9fgYDrjOLrkqr\nxznfvqaiKiIi4umcDbD3P7D5XbOkGS7zuJe/eUZx0H9DwsSfVNCOlR/jmmXXUOeq48ULX+SSrpc0\nU3g3cNabQwT2fAK7PjSHCJzgGwr9roTBPzcnZJ1u4pe0OBVVFVUREWlrKotg01uQ/r9QlnXyeHwS\nDL3FPIPo1zx/+x748gFWHl3JqOhRvH7p69hay2x7lwsyU2HnB2Zp/e4QiJDOMPgGGHwTRPa1LqOo\nqKqoiohIm5GzFVIXmZOInLXmsYAIGP5LGHorRPRs1i+XmpPKHV/cgcPm4P2r3qd3x97N+votxuWC\noynm0Iidy6D2O8MDYoaY5X7QDeZNCKRFqaiqqIqISGtmGLB/Faz7CxxZd/J4zFBI+q159tS7+ceM\nNrgauOHjG9hfsp+b+97M40mPN/vXsER9jTmedds/zaW6TtzQwOEDfa+EYbdC94s0NKCFnG9f06x/\nERERK7mcsGuZWVBzt5vH7F7Q/1pIuttcAN+Nl+H/ufef7C/ZTwffDtw39D63fZ0W5+0HA641t8oi\n2PFvc4xv7nbY+X/mFhoPQ39hltYOXaxOLKehM6oiIiJWaKg1Z+5/8xIUHzKPeQfCyNtg9L3mOqNu\nVlhdyFUfXEVFfQUzRs/gxj43uv1rWi5nK2x6F7a//52VA2zmcl4jfmOunODwtjJhm6QzqiIiIq1B\nQx1sWQxrnoeyY+Yx/zDz8v6oO1t0/OSLG16kor6CAeEDuL7X9S32dS0VMwSmDIFLZ5mrBmx627y1\n7P6V5hYUZZ5lHf4rc/1ZsZTOqIqIiLQEZwNsXQJr5p28c1RwDIy9H0b8GnwCWzTOhtwN3Pb5bdiw\n8d6U9xgYMbBFv75HKTpgDgvYvBgq808e736heZa1zxTw8rEoXNugyVQqqiIi4olcTnP2/ld/PnmJ\nPzASJjwII25zywSpH1PvqufGj29kf8l+buh9AzPHzGzxDB7JWQ97P4ONb8GB1cC3FSkg4tuzrL9u\n9hUX2gsVVRVVERHxJIYBGStg5ZOQv9M8FhAO4x+Akbef152jmss7O9/huQ3P0cG3Ax9f+zEd/DpY\nlsVjFR/59izr/2t6Q4FuE8xhAf2uAm9/6/K1MiqqKqoiIuIpjm2EFTNPLjPlFwrjpsKou8A3yNJo\n+VX5XL3sairrK3lyzJNc37udjE09X84Gc3mrjW/B/hUn7wrmF2re/Wr4ryB6kKURWwNNphIREbFa\n0QFY9ZR5hyQAh6+5xNT4BzxmkfnnNzxPZX0lgyMGc12v66yO4/kcXtD3Z+ZWesxcqWHTu1B6FNIW\nmVvMUHOJq4HXe8x/57ZCZ1RFRER+qupi+HqeWVpcDYDNHNN44WPQId7qdI3SctK4/YvbsWHjH1f+\ng/7h/a2O1Dq5XHDoK9j0Duz+BFz15nGHj7m81dBbzOWutMxVI51RFRERaWnOetjwJnw12yyrAD0v\ngUuegqgB1mb7nnp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rnoaaUszL/L/69jJ/uNXpPFJhdSF//OqPNBgNXNbtMn7Z/5dWRxKx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\nVURERES80v8HvD6MsdkEpJgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11b962908>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(ts, angles_s)\n",
"plt.plot(times, angles, 'x')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plt.plot(ts, omega_s)\n",
"plt.plot(times, omega, 'x')"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11b36fe80>,\n",
" <matplotlib.lines.Line2D at 0x11b361c88>,\n",
" <matplotlib.lines.Line2D at 0x11b54e160>]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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BGDgNxj6qe0Ct1HY0XPvG6Z2Vvv6TzyOk5aWxO2c3DpuDUYmjfH5+qRuGxg/F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\niHjc/wfVwKbc8GhmLQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11b36fdd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(ts, omega_s)\n",
"plt.plot(times, omega, 'x')"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11b582208>,\n",
" <matplotlib.lines.Line2D at 0x11b54e470>,\n",
" <matplotlib.lines.Line2D at 0x11b73bb70>]"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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gdYO4FX+L8vnLM6/DPGr51LJjxfbRrkw73B3cCY8J58jtvUzu54+ro5FdZ2/z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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11b582240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(ts, alpha_s)\n",
"plt.plot(times, alpha, 'x')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@kookma
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kookma commented Mar 2, 2022

Very useful! Thank you for sharing! I would appreciate if you could add references to each problem, then one can see the physics/math behind it!

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