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Quaternion rotation
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Quaternion Rotation"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## quaternion rotation: \n#### given vectors and angle: \n<pre>\nvector: P = [px, py, pz], (P should be normalized: P / |P|) \nunit vector (rotation axis): U = [ux, uy, uz], (U should be normalized: U / |U|) \nrotation angle: θ \n</pre>\n#### quaternion equations: \n<pre>\nquaternion: P = [pw, px, py, pz]\nquaternion: Q = [cos(θ/2), ux * sin(θ/2), uy * sin(θ/2), uz * sin(θ/2)]\nquaternion: Q<sup>-1</sup> = [cos(θ/2), ux * sin(θ/2), uy * sin(θ/2), uz * sin(θ/2)]\n\nquaternion multiplication: q1 * q2 = [q1w, q1x, q1y, q1z] * [q2w, q2x, q2y, q2z] \n = [[q1w * q2w - q1x * q2x - q1y * q2y - q1z * q2z],\n [q1w * q2x + q1x * q2w + q1y * q2z - q1z * q2y],\n [q1w * q2y - q1x * q2z + q1y * q2w + q1z * q2x], \n [q1w * q2z + q1x * q2y - q1y * q2x + q1z * q2w]]\n\nquaternion rotation: [w, x, y, z] = Q * P * Q<sup>-1</sup>, (use quaternion multiplication: (Q * P) * Q<sup>-1</sup>)\n</pre>\n#### new vector after quaternion rotation: \n<pre>\nvector: [x, y, z]\n</pre>"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Quaternion rotation: Vector A with Unit vector and Rotation angle"
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2019-12-24T02:56:32.687981Z",
"end_time": "2019-12-24T02:56:33.051583Z"
},
"trusted": true
},
"cell_type": "code",
"source": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\n%matplotlib inline",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-21T15:19:32.450750Z",
"start_time": "2019-12-21T15:19:32.377997Z"
},
"trusted": true
},
"cell_type": "code",
"source": "A = np.array([1, -1, 1]) # initial vector A (arbitary vector)\nAs = np.linalg.norm(A) # scalar of A: |A|\nAn = A / As # normalization: should be (sum(x**2 + y**2 + z**2))**0.5 = 1.0\n\nU = np.array([-0.1, -0.9, 0.2]) # unit vector (not normalized)\nUs = np.linalg.norm(U) # scalar of U: |U|\nUV = U / Us # unit vector (normalized)\n\n# quaternion multiplication function\ndef QbyQ(q1, q2): # q = [w, x, y, z]\n w = q1[0]*q2[0] - q1[1]*q2[1] - q1[2]*q2[2] - q1[3]*q2[3]\n i = q1[0]*q2[1] + q1[1]*q2[0] + q1[2]*q2[3] - q1[3]*q2[2]\n j = q1[0]*q2[2] - q1[1]*q2[3] + q1[2]*q2[0] + q1[3]*q2[1]\n k = q1[0]*q2[3] + q1[1]*q2[2] - q1[2]*q2[1] + q1[3]*q2[0]\n return np.array([w, i, j, k])\n\n# quaternion rotation function\ndef QPQc(P, UV, t): # P: quaternion, UV: unit vector, t: rotation angle theta\n q = [np.cos(t/2), UV[0] * np.sin(t/2), UV[1] * np.sin(t/2), UV[2] * np.sin(t/2)]\n qc = [np.cos(t/2), -UV[0] * np.sin(t/2), -UV[1] * np.sin(t/2), -UV[2] * np.sin(t/2)]\n qP = QbyQ(q, P)\n result = QbyQ(qP, qc)\n return result\n\nQA = np.insert(An, 0, 0) # quaternion of An: [0, x, y, z]\ntheta = np.deg2rad(45) # rotation angle\nQB = QPQc(QA, UV, theta) # quaternion rotation for An with UV and theta\nBn = QB[1:] # vectorize the quaternion result\nB = Bn * As # new vector as same scalar as initial vector A",
"execution_count": 380,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-21T15:20:31.164415Z",
"start_time": "2019-12-21T15:20:30.588950Z"
},
"code_folding": [],
"run_control": {
"marked": false
},
"trusted": true
},
"cell_type": "code",
"source": "# plot \ndef plot_base(elev=25, azim=-70):\n fig = plt.figure(figsize=(10, 10))\n ax = fig.add_subplot(111, projection='3d')\n ax.view_init(elev=elev, azim=azim)\n ax.set(xlim=(-1, 1), ylim=(-1 ,1), zlim=(-1, 1))\n ax.set(xlabel='X', ylabel='Y', zlabel='Z')\n ax.xaxis.pane.fill = ax.yaxis.pane.fill = ax.zaxis.pane.fill = False\n\n t = np.linspace(0, 2*np.pi, 128+1)\n alpha = 0.7\n ax.plot(np.cos(t), np.sin(t), [0]*len(t), linestyle=':', c='red', alpha=alpha)\n ax.plot(np.cos(t), [0]*len(t), np.sin(t), linestyle=':', c='red', alpha=alpha)\n ax.plot([0]*len(t), np.cos(t), np.sin(t), linestyle=':', c='red', alpha=alpha)\n ax.plot([-1, 1], [0, 0], [0, 0], linestyle=':', c='red', alpha=alpha)\n ax.plot([0, 0], [-1, 1], [0, 0], linestyle=':', c='red', alpha=alpha)\n ax.plot([0, 0], [0, 0], [-1, 1], linestyle=':', c='red', alpha=alpha)\n return ax\n\nax = plot_base()\nax.plot([0, A[0]], [0, A[1]], [0, A[2]], c='b', alpha=0.4) # vector A\nax.scatter(A[0], A[1], A[2], c='b', alpha=0.4)\nax.text(A[0], A[1], A[2], s=' initial vector A', va='top')\nax.plot([0, An[0]], [0, An[1]], [0, An[2]], c='b') # vector A normalized\nax.scatter(An[0], An[1], An[2], c='b')\nax.text(An[0], An[1], An[2], s=' normalized vector An', va='top')\n\nax.plot([0, UV[0]], [0, UV[1]], [0, UV[2]], c='r') # unit vector\nax.scatter(UV[0], UV[1], UV[2], c='r')\nax.text(UV[0], UV[1], UV[2], s=' unit vector', va='top')\n\nax.plot([0, B[0]], [0, B[1]], [0, B[2]], c='g', alpha=0.4) # vector B\nax.text(B[0], B[1], B[2], s='initialized vector B ', ha='right', va='top')\nax.scatter(B[0], B[1], B[2], c='g', alpha=0.4)\nax.plot([0, Bn[0]], [0, Bn[1]], [0, Bn[2]], c='g') # vector B normalized\nax.scatter(Bn[0], Bn[1], Bn[2], c='g')\nax.text(Bn[0], Bn[1], Bn[2], s='normalized vector Bn ', ha='right', va='top')\n\nArc = [QPQc(QA, UV, t) for t in np.linspace(0, theta, 33)] # arc between A and B\narw, arx, ary, arz = np.array(Arc).T\nax.plot(arx, ary, arz, linestyle='--', c='b', alpha=0.6)\nax.plot(arx*As, ary*As, arz*As, linestyle='--', c='b', alpha=0.4)",
"execution_count": 383,
"outputs": [
{
"data": {
"text/plain": "[<mpl_toolkits.mplot3d.art3d.Line3D at 0x11ed08048>]"
},
"execution_count": 383,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": "<matplotlib.figure.Figure at 0x11eb1f4e0>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Find Unit vector and Rotation angle from Two vectors"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-23T05:23:51.521394Z",
"start_time": "2019-12-23T05:23:51.442333Z"
},
"code_folding": [
0
],
"trusted": true
},
"cell_type": "code",
"source": "# find unit vector and rotation angle for two vectors A and B\nA = np.array([1, -1, 0.2]) # start point A\nAs = np.linalg.norm(A) # scalar of A: |A|\nAn = A / As # normalization\n\nB = np.array([0.4, -0.1, 1.1]) # end point B\nBs = np.linalg.norm(B) # scalar of B: |B|\nBn = B / Bs # normalization\n\n# find unit vector for An-Bn rotation\nAnxBn = np.cross(An, Bn) # orthogonal vector to An-Bn\nUV = AnxBn / np.linalg.norm(AnxBn) # unit vector (normalized): rotation axis \n\n# find rotation angle about An-Bn\n# cos_t = (An dot Bb) / (|An|*|Bn|) # (|An|*|Bn|) = An * Bn = 1 * 1 = 1\ncos_AnBn = np.dot(An, Bn)\ntheta_AnBn = np.arccos(cos_AnBn) # angle between An and Bn\n\n# reproduct A-B rotation\nQa = np.insert(An, 0, 0) # quaternion of An: [0, x, y, z]\nQb = QPQc(Qa, UV, theta_AnBn) # quaternion rotation for An with UV and theta_AB\nBn_new = Qb[1:] # new Bn vector (normalized): [bx, by, bz]\nB_new = Bn_new * Bs # new B vector\n\nprint('unit vector:', UV)\nprint('theta (degrees):', np.rad2deg(theta_AnBn))\nprint('initial vector B:', B)\nprint('new vector B :', B_new) ",
"execution_count": 665,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "unit vector: [-0.71262682 -0.67303645 0.1979519 ]\ntheta (degrees): 64.5883294834531\ninitial vector B: [ 0.4 -0.1 1.1]\nnew vector B : [ 0.4 -0.1 1.1]\n"
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-23T05:23:55.165213Z",
"start_time": "2019-12-23T05:23:54.430237Z"
},
"code_folding": [],
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "# interactive plot with ipywidgets\nfrom ipywidgets import interact\n%matplotlib inline\n\nsteps = 33\nArc = np.array([QPQc(Qa, UV, t) for t in np.linspace(0, theta_AnBn, steps)]).T # arc An-Bn\n_, arx, ary, arz = Arc\nABs = np.linspace(As, Bs, steps) # scalar transition from A to B\nABx = arx * ABs # x term for arc A-B\nABy = ary * ABs # y term for arc A-B\nABz = arz * ABs # z term for arc A-B\n\n@interact(idx=(0, steps-1, 1), elev=(0, 180, 1), azim=(-180, 180, 1))\ndef two_vec(idx=10, elev=25, azim=96):\n ax = plot_base(elev, -azim)\n\n ax.plot([0, A[0]], [0, A[1]], [0, A[2]], c='b', alpha=0.4) # vector A\n ax.scatter(A[0], A[1], A[2], c='b', alpha=0.4) # point A\n ax.text(A[0], A[1], A[2], s=' initial vector A')\n ax.plot([0, An[0]], [0, An[1]], [0, An[2]], c='b') # vector An\n ax.scatter(An[0], An[1], An[2], c='b') # point An\n ax.text(An[0], An[1], An[2], s='normalized vector An ', ha='right', va='top')\n\n ax.plot([0, UV[0]], [0, UV[1]], [0, UV[2]], c='r') # unit vector\n ax.scatter(UV[0], UV[1], UV[2], c='r')\n ax.text(UV[0], UV[1], UV[2], s='unit vector ', ha='right', va='top')\n\n ax.plot([0, B[0]], [0, B[1]], [0, B[2]], c='g', alpha=0.4) # vector B\n ax.text(B[0], B[1], B[2], s='initialized vector B ', ha='right', va='center')\n ax.scatter(B[0], B[1], B[2], c='g', alpha=0.4) # vector B\n ax.plot([0, Bn[0]], [0, Bn[1]], [0, Bn[2]], c='g') # vector Bn\n ax.scatter(Bn[0], Bn[1], Bn[2], c='g') # vector Bn\n ax.text(Bn[0], Bn[1], Bn[2], s='normalized vector Bn ', ha='right', va='center')\n \n ax.plot([0, arx[idx]], [0, ary[idx]], [0, arz[idx]], color='magenta') # vector An (move)\n ax.plot([0, arx[idx]*As], [0, ary[idx]*As], [0, arz[idx]*As], c='m', alpha=0.4) # move A (move)\n ax.scatter(arx[idx]*As, ary[idx]*As, arz[idx]*As, c='m', alpha=0.4) # point A (move)\n ax.scatter(arx[idx], ary[idx], arz[idx], c='m') # point An (move)\n ax.plot(arx[:idx+1], ary[:idx+1], arz[:idx+1], linestyle='--', c='b', alpha=0.7) # arc An-Bn\n ax.plot(arx[:idx+1]*As, ary[:idx+1]*As, arz[:idx+1]*As, ls='--', c='b', alpha=0.7) # arc A-A\n rate = As + (Bs - As) * idx / steps\n ax.scatter(arx[idx]*rate, ary[idx]*rate, arz[idx]*rate, c='m') # point A-B\n ax.plot(ABx[:idx+1], ABy[:idx+1], ABz[:idx+1], ls='--', c='m', alpha=0.9) # arc A-B",
"execution_count": 666,
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "2729d5b0bbed4ec2b32239abccfa3db8",
"version_major": 2,
"version_minor": 0
},
"text/plain": "interactive(children=(IntSlider(value=10, description='idx', max=32), IntSlider(value=25, description='elev', …"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2019-12-24T02:59:22.019898Z",
"end_time": "2019-12-24T02:59:22.317062Z"
},
"code_folding": [],
"trusted": true,
"run_control": {
"marked": false
}
},
"cell_type": "code",
"source": "# 2D explanation diagram\ncase = False\n\nfig = plt.figure(figsize=(6,6))\nax = fig.add_subplot(111)\nax.axis([-1.5, 1.5, -1.3, 1.7], 'equal')\nax.grid()\nt = np.linspace(0, np.pi*2, 129)\nax.plot(np.cos(t), np.sin(t), 'r:')\nax.text(0,0, s='O ', va='top', ha='right')\nA = [1.0, 1.1]\nB = [-0.4, 1.1]\nAs = np.linalg.norm(A)\nBs = np.linalg.norm(B)\nAn = np.array(A) / As\nBn = np.array(B) / Bs\n\nax.plot([0, A[0]], [0, A[1]], c='b') # A-O\nax.scatter(A[0], A[1], c='b') # A\nax.text(A[0], A[1], s=' A', va='center') # A text\nax.scatter(An[0], An[1], c='b') # An\nax.text(An[0], An[1], s=' An', va='center') # An text\n\nax.plot([0, B[0]], [0, B[1]], c='g') # B-O\nax.scatter(Bn[0], Bn[1], c='g') # Bn\nax.text(Bn[0], Bn[1], s='Bn ', ha='right', va='center') # Bn text\n\nif case:\n ax.plot([0, Bn[0]*As], [0, Bn[1]*As], c='g') # B as same scaler as A\n ax.scatter(Bn[0]*As, Bn[1]*As, c='g')\n ax.text(Bn[0]*As, Bn[1]*As, s='B ', ha='right', va='center')\nelse:\n ax.scatter(B[0], B[1], c='g') # B\n ax.text(B[0], B[1], s='B ', ha='right', va='center') # B text\n rad_An = np.arccos(An[0])\n rad_Bn = np.arccos(Bn[0])\n t = np.linspace(rad_An, rad_Bn, 33)\n ax.plot(As*np.cos(t), As*np.sin(t), c='b', ls='--', lw=1) # arc A-A'\n ax.scatter(Bn[0]*As, Bn[1]*As, marker='x', c='b') # A' x marker\n ax.text(Bn[0]*As, Bn[1]*As, s='A\\' ', ha='right', va='center') # A' text\n ABs = np.linspace(As, Bs, 33)\n ax.plot(ABs*np.cos(t), ABs*np.sin(t), c='m', ls='--', lw=1) # arc A-B",
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x10dd5e438>",
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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"kernelspec": {
"name": "py36",
"display_name": "py36",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.6.7",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"gist": {
"id": "",
"data": {
"description": "Quaternion rotation",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
numpy
matplotlib
ipywidgets
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