Active vs. passive rotation

active_passive.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pytransform3d.rotations as pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = pr.matrix_from_angle(2, 0.5 * np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  0.],\n",
       "       [-1.,  0.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(R, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_state = random.RandomState(0)\n",
    "points = random_state.randn(10, 2) * 0.1 + np.array([[1, 1]])\n",
    "points = np.hstack((points, np.zeros((len(points), 1))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_coordinate_frame(ls=\"-\"):\n",
    "    subplot(111, aspect=\"equal\")\n",
    "    plot([0, 2], [0, 0], c=\"r\", ls=ls)\n",
    "    plot([0, 0], [0, 2], c=\"g\", ls=ls)\n",
    "    xlim((-2, 2))\n",
    "    ylim((-2, 2))\n",
    "    grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate_points(R, points):\n",
    "    return points.dot(R.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_points(points):\n",
    "    scatter(points[:, 0], points[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7145a07ac8>]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_coordinate_frame()\n",
    "plot_points(points)\n",
    "# new coordinate frame\n",
    "plot([-0.05, -0.05], [0, 2], c=\"r\", ls=\"--\")\n",
    "plot([-2, 0], [0.05, 0.05], c=\"g\", ls=\"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7146316f60>]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rotated_points = rotate_points(R, points)\n",
    "plot_coordinate_frame(ls=\"--\")\n",
    "plot_points(rotated_points)\n",
    "# old coordinate frame\n",
    "plot([0, 0], [-0.05, -2], c=\"r\")\n",
    "plot([0, 2], [-0.05, -0.05], c=\"g\")"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}