demo_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Helper functions for visualization purpose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from my_display import display_line\n",
    "from my_display import display_lines\n",
    "from my_display import display_points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initialize scan data scan_sim (simulation) & scan_real (real data from laser rangefinder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Scan_Data(object):\n",
    "    '''\n",
    "    A mockup of the ros_scan data structure\n",
    "    '''\n",
    "    def __init__(self, ranges, angle_min, angle_max, angle_increment):\n",
    "        self.ranges = ranges\n",
    "        self.angle_min = angle_min\n",
    "        self.angle_max = angle_max\n",
    "        self.angle_increment = angle_increment\n",
    "\n",
    "ranges1 = [0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 0.01899999938905239, 1.5169999599456787, 1.5379999876022339, 1.5509999990463257, 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2.700000047683716, 2.753000020980835, 2.753000020980835, 2.75600004196167, 2.7720000743865967, 20.0, 20.0, 20.0, 20.0, 20.0, 0.007000000216066837, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 2.6659998893737793, 2.6600000858306885, 2.6600000858306885, 2.6549999713897705, 2.6549999713897705, 0.007000000216066837, 2.6549999713897705, 2.6549999713897705, 2.63100004196167, 2.630000114440918, 2.63100004196167, 2.63100004196167, 2.630000114440918, 2.621000051498413, 2.617000102996826, 2.614000082015991, 2.6010000705718994, 2.5999999046325684, 2.5999999046325684, 2.5959999561309814, 2.5950000286102295, 2.5940001010894775, 2.5910000801086426, 2.5910000801086426, 2.5789999961853027, 2.5739998817443848, 2.5739998817443848, 2.572000026702881, 2.569000005722046, 2.562999963760376, 2.562000036239624, 2.562000036239624, 2.563999891281128, 2.562000036239624, 2.562999963760376, 2.563999891281128, 2.562999963760376, 2.562999963760376, 2.562999963760376, 2.565000057220459, 2.562000036239624, 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    "angle_min1 = -2.35619449615\n",
    "angle_max1 = 2.09234976768\n",
    "angle_increment1 = 0.00613592332229\n",
    "scan_real = Scan_Data(ranges1, angle_min1, angle_max1, angle_increment1)\n",
    "\n",
    "ranges2 = [3.1762819290161133, 3.103274345397949, 3.0388646125793457, 2.9823038578033447, 2.9329640865325928, 2.89031982421875, 2.8539328575134277, 2.823441743850708, 2.798551559448242, 2.779027223587036, 2.764688014984131, 2.7554025650024414, 2.751087188720703, 2.7517027854919434, 2.7572555541992188, 2.767794609069824, 2.7834160327911377, 2.80426287651062, 2.830528974533081, 2.86246395111084, 2.900378465652466, 2.944652557373047, 2.995744466781616, 3.054204225540161, 3.120687961578369, 3.1959784030914307, 3.2810096740722656, 3.376899003982544, 3.484987735748291, 3.6068944931030273, 3.744584560394287, 3.8952274322509766, 4.062768936157227, 4.26259708404541, 4.500875949859619, 4.774260520935059, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 4.090345859527588, 3.168231964111328, 2.6013054847717285, 2.2040998935699463, 1.9220681190490723, 1.7043126821517944, 1.530637264251709, 1.3885233402252197, 1.292419195175171, 1.1920390129089355, 1.1161623001098633, 1.0444583892822266, 1.0320638418197632, 1.0826857089996338, 1.1179065704345703, 1.1707769632339478, 1.1833229064941406, 1.24471116065979, 1.3293348550796509, 1.390398383140564, 1.4890056848526, 1.585628628730774, 1.7008298635482788, 1.872342824935913, 2.0380444526672363, 2.26603627204895, 2.562479019165039, 2.928550958633423, 3.0290300846099854, 2.9977591037750244, 2.984292507171631, 2.967543840408325, 2.9562439918518066, 2.9502906799316406, 2.9496304988861084, 2.9542572498321533, 2.9642128944396973, 2.9795870780944824, 3.0005204677581787, 3.0272068977355957, 3.059898614883423, 3.0989115238189697, 3.1446335315704346, 3.1975338459014893, 3.258176565170288, 3.3272345066070557, 3.4055111408233643]\n",
    "angle_min2 = -2.09439516068\n",
    "angle_max2 = 2.09439516068\n",
    "angle_increment2 = 0.0423110127449\n",
    "scan_sim = Scan_Data(ranges2, angle_min2, angle_max2, angle_increment2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preprocessing step\n",
    "\n",
    "Transformation coordinates from polar coordinate system to cartesian coordinate system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin\n",
    "from math import cos\n",
    "\n",
    "maximum_range = 4.3\n",
    "minimum_range = 0.1\n",
    "\n",
    "class Coordinates(object):\n",
    "    '''\n",
    "    Store coordinates in cartesian coordinate system as well as in polar coordinate system\n",
    "    '''\n",
    "    def __init__(self, x, y, theta, rho):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.theta = theta\n",
    "        self.rho = rho\n",
    "\n",
    "        \n",
    "def preprocess(scan, maximum_range):\n",
    "    x = []\n",
    "    y = []\n",
    "    theta = []\n",
    "    rho = []\n",
    "    for i in range(len(scan.ranges)):\n",
    "        rho_i = scan.ranges[i]\n",
    "        if rho_i < minimum_range or rho_i > maximum_range:\n",
    "            continue\n",
    "        theta_i = scan.angle_min + i * scan.angle_increment\n",
    "        x_i = rho_i * cos(theta_i)\n",
    "        y_i = rho_i * sin(theta_i)\n",
    "        x.append(x_i)\n",
    "        y.append(y_i)\n",
    "        theta.append(theta_i)\n",
    "        rho.append(rho_i)\n",
    "    coordinates = Coordinates(x, y, theta, rho)\n",
    "    return coordinates    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize scan data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data in simulation environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coordinates_sim = preprocess(scan_sim, maximum_range)\n",
    "display_points(coordinates_sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data in real-world environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAEWxJREFUeJzt3X+MVeWdx/HPhwGLgyO0Mv5YIKDRGNG4mkyEG//ZWlOmXX+kNk1qut0m1kzXLqkljVJrsoRsttnURLaJJs3NlPSPNW02KaSNVhCztsZ0RAcXEQQbQiVQrUyxCEIrMHz3jzPT+cE4d5hzuOfe575fyc05595zn/MdJZ955jnPOccRIQBAOmaUXQAAoFgEOwAkhmAHgMQQ7ACQGIIdABJDsANAYgh2AEgMwQ4AiSHYASAxM8s46Pz582PJkiVlHLp5HT8uHTggDQ6OvNfWJi1aJM2ZU15dAOpm27Ztf4qIzlr7lRLsS5YsUX9/fxmHBoCmZXv/VPZjKKYIfX3S8uXS9ddny76+sisC0MJK6bE3nb4+adUq6dixiT8/eFA6enRke+1aadOm+tQGAOMQ7KN9XICPD+6JzJ0rLVggdXRIa9acvxoBoIbWDPbpBPhwcE+ko0Nat06qVIqtEwCmoTWCvVqVHn5Y+uQnpfb2cw9wghtAE0k/2Pv6pJUrpVOnpA8+GHmfAAeQqLSDva9PuvPOLNSH53y3txPgAJKWdrCvWiUdPixdfHE2S4UgB9ACWmMe+3XXEeoAWkbawb5unbRiRbYEgBaRdrBXKtmc8rVruRoUQMtIe4xdykJ98+ZsnatBAbSA9IN9+CpQrgYF0CLSHoqRGI4B0HLS77FLDMcAaCmtEewMxwBoIekPxUgMxwBoKa3RY5cYjgHQMlqjxy5lPfZly6QjR+i1A0ha6wR7pSLNmydt3Zr13gEgUa0T7JJ0zz3SJZdkSwBIVO5gtz3b9iu2X7e9y3bjdoc3bMju9rhhQ9mVAMB5U8TJ048k3RYRH9qeJekl289GxMsFtF0spj0CaAG5e+yR+XBoc9bQK/K2e14w7RFACyhkuqPtNknbJF0t6cmI2FpEu+cF0x4BJK6Qk6cRMRgRN0laKOkW2zeM38d2j+1+2/0DAwNFHHZ6mPYIIHGFzoqJiCOSfi2pe4LPqhHRFRFdnZ2dRR723DDtEUDiipgV02l73tD6hZJul7Qnb7vnFb12AAkrosd+haQXbO+Q9KqkLRHxdAHtnj/02gEkLPfJ04jYIenmAmqpL6Y+AkhU69wEbLxKhVkxAJLUWrcUAIAWQLADQGIIdgBIDMEOAIkh2AEgMQQ7ACSGYAeAxBDsAJAYgh0AEkOwA0BiCHYASAzBDgCJIdgBIDEEOwAkhmAHgMQQ7ACQGIIdABJDsANAYgh2AEgMwQ4Aickd7LYX2X7B9m7bu2w/WERhAIDpmVlAG6clfSciXrPdIWmb7S0R8WYBbQMAzlHuHntEvBsRrw2tH5O0W9KCvO0CAKan0DF220sk3Sxp6wSf9djut90/MDBQ5GEBAKMUFuy2L5L0c0nfjoij4z+PiGpEdEVEV2dnZ1GHBQCMU0iw256lLNSfiogNRbQJAJieImbFWNKPJe2OiMfzlwQAyKOIHvutkr4q6Tbb24deny+gXQDANOSe7hgRL0lyAbUAAArAlacAkBiCHQASQ7ADQGIIdgBIDMEOAIkh2AEgMQQ7ACSGYAeAxBDsAJAYgh0AEkOwA0BiCHYASAzBDgCJIdgBIDEEOwAkhmAHgMQQ7ACQGIIdABJDsANAYgh2AEhMIcFue73tQ7Z3FtEeAGD6iuqx/0RSd0FtAQByKCTYI+JFSe8X0RYAIB/G2AEgMXULdts9tvtt9w8MDNTrsADQcuoW7BFRjYiuiOjq7Oys12EBoOUwFAMAiSlquuNPJfVJutb2QdtfL6JdAMC5m1lEIxFxbxHtAADyYygGABJDsANAYgh2AEgMwQ4AiSHYASAxBDsAJIZgB4DEEOwAkBiCHQASQ7ADQGIIdgBIDMEOAIkh2AEgMQQ7ACSGYAeAxBDsAJAYgh0AEkOwA0BiCHYASAzBDgCJKSTYbXfbfsv2XtvfLaJNAMD05A52222SnpT0OUlLJd1re2nedgEA01NEj/0WSXsjYl9EnJT0M0l3F9AuAGAaigj2BZIOjNo+OPQeAKAERQS7J3gvztrJ7rHdb7t/YGCggMMCACZSRLAflLRo1PZCSe+M3ykiqhHRFRFdnZ2dBRwWADCRIoL9VUnX2L7S9gWSvizplwW0CwCYhpl5G4iI07ZXStosqU3S+ojYlbsyAMC05A52SYqIX0n6VRFtAQDy4cpTAEgMwQ4AiSHYASAxBDsAJIZgR+Po65MuuUSypTlzpHnzpNWrpe7u7DMAU1LIrBggl2pVeuAB6cyZkfdOnMiW69ZJp05l65s21b82oAkR7ChPX590xx3S+++f/Vl7uzRrlvSNb0ivvy6tWVP/+oAmRbCj/qpV6Vvfkj766OzP5s6Vnn1WqlTqXxeQCMbYUX/f/ObEof6Vr0hHjhDqQE702FFf1ao0ODj2vc9+Vtq8uZx6gAQR7Kivhx8eux1n3eEZQE4MxaC+Fox6Bsstt5RXB5Awgh311dsrrVgh/fa30tatZVcDJImhGNRXpcJ8dOA8o8cOAIkh2AEgMQQ7ACSGYAeAxBDsAJAYgh0AEkOwA0BicgW77S/Z3mX7jO2uoooCAExf3h77Tkn3SHqxgFoAAAXIdeVpROyWJNvFVAMAyK1uY+y2e2z32+4fGBio12EBoOXU7LHbfl7S5RN89GhE/GKqB4qIqqSqJHV1dXGvVgA4T2oGe0TcXo9CAADFYLojACQm73THL9g+KKki6RnbPN8MAEqWd1bMRkkbC6oFAFAAhmIAIDEEOwAkhmAHgMQQ7I2kWpXmz8+WADBNBHsjeegh6fDhbAkA00SwN5KZM8cuAWAaCPZG8uc/j10CwDQQ7I1k1qxsGcE4O4BpI9gbydVXj6yvWlVeHQCaGsHeSHp7R9ZPny6vDgBNjWBvJJWKNHt2tn7qlNTXV249AJoSwd5orroqW0ZI999fbi0AmhLB3mh6e6XhRw3u21duLQCaEsHeaCoV6ROfKLsKAE2MYG9Ew8MxJ08y7RHAOSPYG1Fvr9TWJp05w+0FAJwzgr0RVSpSZ2e23t5ebi0Amg7B3qiOHcuWhw4x7RHAOSHYG9XixdnyzBmuQgVwTgj2RtXbK82Zk60P994BYApyBbvtx2zvsb3D9kbb84oqrOVVKiO9dgA4B3l77Fsk3RARN0r6naRH8peEvzlxYuwSAKYgV7BHxHMRMXy3qpclLcxfEv5mYGDsEgCmoMgx9vskPVtgexg9FMPMGABTVDPYbT9ve+cEr7tH7fOopNOSnpqknR7b/bb7B+iBTk1vr3TxxdLx48yMATBlNR+uGRG3T/a57a9JukPSZyIiJmmnKqkqSV1dXR+7H0apVKRPfUo6elR6772yqwHQJPLOiumWtFrSXRHBGb7zYfj5pwcOMBwDYEryjrE/IalD0hbb223/qICaMNoPfpDdN2ZwkOEYAFNScyhmMhFxde29kEtPj/TDH0pvvsmFSgCmhCtPm0FHx9glAEyCYG8G69ZJK1ZkSwCogWBvBm+8IfX3Z0sAqIFgbwYPPSQdPsxDNwBMCcHeDBYO3anhww95VN5UVavS3LnSlVdKy5czVRQthWBvBr290qxZ2b3ZV65s7ZAaDuwrrpAuumhkOT7Av/e97MKut9+Wtm6V1q4ttWygngj2ZlCpSE88kc1nP3Uq3fnsfX1Sd7e0evXZ4X3hhdnrgQeywP7jH7NbLQwvxwf497+f3Y5hyRJp2TJpzZoyfzKgrjzJXQDOm66urujv76/7cZve9ddn89mXLpV27Sq7mnyq1ewX1Jkz0rx52Rz9wUHpr3+t/d22tuyZsMeOZVNAjx3Lti+7LJs5VKmc//qBEtjeFhFdtfbLdYES6mx4Hvsf/pD1bpslwKrV7MRve7t05Ej23smTWahLWa97vPHhPfy9q67Khqaa5WcHSkCwN5N167Khig8+yHq7L79cdkXZL5j775f27cu2h3vfwz3pjo6R4D56dOx3Z8yQLrhg5DudnVn4d3TQ8wZyINibSaUiXXddNpZcT8PhvX//2N7zvHnZQ0AGB0f2HQ7x48fHLiXp8svpeQN1QLA3m/vuk/buzZZF6+vL/hJ4770ssIdDfPSwyeigHg7x4Z63NHGP/S9/yW5m1tNTfM0AzkKwN5v167OLldavzxeU43vhE528HB3iM2Zks1LG99gJbaDhEOzNas+eqZ9AHR3iw+PY+/dPPFwiSbNnZycvh0O8rU16/HHCG2gSBHuzWbdOuvPOrNe+dq20aVPt76xdm02TlM4O8RkzpEsvZcogkBAuUGo2lUp28U17u/Sb32Rz22tdibpmTTb3fc6c7IKdpUuz17Jl0ksvSe++m92u4Pe/z2baEOpAU6PH3ow2bJBODD2J8M03a/fcK5Xmv6AJwJQR7M1ozZrsGaj790uLF3O5PIAxCPZmRA8cwCQYYweAxOQKdtv/bnuH7e22n7P9d0UVBgCYnrw99sci4saIuEnS05L+rYCaAAA55Ar2iBh9V6c5kup/D2AAwBi5T57a/g9J/yzpA0mfzl0RACCXmj1228/b3jnB625JiohHI2KRpKckrZyknR7b/bb7BwYGivsJAABjFPYEJduLJT0TETfU2pcnKAHAuZvqE5Tyzoq5ZtTmXZL25GkPAJBf3jH2/7R9raQzkvZL+pf8JQEA8sgV7BHxxaIKAQAUgytPASAxBDsAJIZgB4DEEOwAkBiCHQASQ7ADQGIIdgBIDMEOAIkh2AEgMQQ7ACSmsLs7ntNB7QFl95YpynxJfyqwvaI1en1S49dIffk1eo3UV9viiOistVMpwV402/1TuZVlWRq9Pqnxa6S+/Bq9RuorDkMxAJAYgh0AEpNKsFfLLqCGRq9PavwaqS+/Rq+R+gqSxBg7AGBEKj12AMCQZILd9mO299jeYXuj7Xll1zSa7S/Z3mX7jO2GObNuu9v2W7b32v5u2fWMZ3u97UO2d5Zdy0RsL7L9gu3dQ/9/Hyy7ptFsz7b9iu3Xh+pbW3ZNE7HdZvv/bD9ddi0Tsf227Tdsb7fdX3Y9tSQT7JK2SLohIm6U9DtJj5Rcz3g7Jd0j6cWyCxlmu03Sk5I+J2mppHttLy23qrP8RFJ32UVM4rSk70TEdZKWS/rXBvtv+JGk2yLi7yXdJKnb9vKSa5rIg5J2l11EDZ+OiJuaYcpjMsEeEc9FxOmhzZclLSyznvEiYndEvFV2HePcImlvROyLiJOSfibp7pJrGiMiXpT0ftl1fJyIeDciXhtaP6YsnBaUW9WIyHw4tDlr6NVQJ9ZsL5T0j5J6y64lFckE+zj3SXq27CKawAJJB0ZtH1QDhVKzsb1E0s2StpZbyVhDwxzbJR2StCUiGqo+Sf8l6WFJZ8ouZBIh6Tnb22z3lF1MLTPLLuBc2H5e0uUTfPRoRPxiaJ9Hlf15/FQ9axs6ds36GowneK+henPNwvZFkn4u6dsRcbTsekaLiEFJNw2dd9po+4aIaIhzFrbvkHQoIrbZ/oey65nErRHxju1LJW2xvWfor8mG1FTBHhG3T/a57a9JukPSZ6KEeZy16mtAByUtGrW9UNI7JdXStGzPUhbqT0XEhrLr+TgRccT2r5Wds2iIYJd0q6S7bH9e0mxJF9v+74j4p5LrGiMi3hlaHrK9UdkwZsMGezJDMba7Ja2WdFdEnCi7nibxqqRrbF9p+wJJX5b0y5Jraiq2LenHknZHxONl1zOe7c7hGWK2L5R0u6Q95VY1IiIeiYiFEbFE2b+//220ULc9x3bH8Lqkz6pxfjFOKJlgl/SEpA5lfyZtt/2jsgsazfYXbB+UVJH0jO3NZdc0dLJ5paTNyk76/U9E7Cq3qrFs/1RSn6RrbR+0/fWyaxrnVklflXTb0L+77UO9z0ZxhaQXbO9Q9ot8S0Q05JTCBnaZpJdsvy7pFUnPRMSmkmuaFFeeAkBiUuqxAwBEsANAcgh2AEgMwQ4AiSHYASAxBDsAJIZgB4DEEOwAkJj/B0lE3nTfpUk/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coordinates_real = preprocess(scan_real, maximum_range)\n",
    "display_points(coordinates_real)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some paramemters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "min_line_points = 10\n",
    "seed_seg_points = 6\n",
    "ortho_threshold = 0.03\n",
    "projected_threshold = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Main Program"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Line class defination and some helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "from math import tan\n",
    "from math import pi\n",
    "\n",
    "\n",
    "class Line(object):\n",
    "    '''\n",
    "    Line representation in the form of ax + by + c = 0\n",
    "    '''\n",
    "    def __init__(self, a, b, c, start, end):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        self.c = c\n",
    "        self.start = start       # start fit point index\n",
    "        self.end = end           # end fit point index\n",
    "        self.leftend = None      # coordinates for left endpoints\n",
    "        self.rightend = None     # coordinates for right endpoints\n",
    "        \n",
    "def fit_line(coordinates, start, end):\n",
    "    n = end - start + 1\n",
    "    temp1, temp2, temp3, temp4, temp5 = 0, 0, 0, 0, 0\n",
    "    for i in range(start, end + 1):\n",
    "        temp1 += coordinates.x[i]\n",
    "        temp2 += coordinates.y[i]\n",
    "        temp3 += coordinates.x[i] ** 2\n",
    "        temp4 += coordinates.y[i] ** 2\n",
    "        temp5 += coordinates.x[i] * coordinates.y[i]\n",
    "    w1 = n * temp5 - temp1 * temp2\n",
    "    w2 = temp2 * temp2 - n * temp4 - temp1 * temp1 + n * temp3\n",
    "    w3 = temp1 * temp2 - n * temp5\n",
    "    if w1 == 0:\n",
    "        a = -1\n",
    "        b = 0\n",
    "        c = temp1 / n\n",
    "    else:\n",
    "        a = (-w2 + sqrt(w2 * w2 - 4 * w1 * w3)) / 2.0 / w1\n",
    "        b = -1\n",
    "        c = (temp2 - a * temp1) / n\n",
    "    line = Line(a, b, c, start, end)\n",
    "    return line\n",
    "\n",
    "\n",
    "def comp_dist_ptp(x1, y1, x2, y2):\n",
    "    '''\n",
    "    Return euclidean distance between two points\n",
    "    '''\n",
    "    return sqrt((x1 - x2) ** 2 + (y1- y2) ** 2)\n",
    "\n",
    "\n",
    "def comp_dist_ptl(x, y, line):\n",
    "    '''\n",
    "    Return the orthogonal distance between a point and a line\n",
    "    '''\n",
    "    return abs(line.a * x + line.b * y + line.c) / sqrt(line.a ** 2 + line.b **2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Seed choosing step\n",
    "\n",
    "Scan through the sacn data, if the candidate satisfies the two given conditions, grow the seed.\n",
    "\n",
    "1. Distance from every point in the seed candidate to the fit line is less than a threshold (ortho_threshold = 0.03)\n",
    "2. Distance from every point in the seed candidate to its projected position on the fit line is less than a threshold (projected_threshold = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def choose_seed(coordinates, start):\n",
    "    end = start + seed_seg_points -1\n",
    "    line = fit_line(coordinates, start, end)\n",
    "    for i in range(start, end + 1):\n",
    "        x = coordinates.x[i]\n",
    "        y = coordinates.y[i]\n",
    "        theta = coordinates.theta[i]\n",
    "        # distance from a point to the fit line\n",
    "        dist1 = comp_dist_ptl(x, y, line)\n",
    "        if dist1 > ortho_threshold:\n",
    "            return None\n",
    "        # compute a point's pojected position on the fit line\n",
    "        if abs(abs(theta) - pi / 2) < 0.00001:  # for tan(theta) does not exist\n",
    "            projected_x = 0\n",
    "            projected_y = line.c\n",
    "        else: \n",
    "            k = tan(theta)\n",
    "            projected_x = line.c / (k - line.a)\n",
    "            projected_y = k * projected_x\n",
    "        # distance from a point to its projected position on the fit line\n",
    "        dist2 = comp_dist_ptp(x, y, projected_x, projected_y)\n",
    "        if dist2 >= projected_threshold:\n",
    "            return None\n",
    "    return line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Seed growing step\n",
    "\n",
    "Grow the seed to its right and left neighbors respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grow_seed(coordinates):\n",
    "    extracted_lines = []\n",
    "    i = 0\n",
    "    while i < len(coordinates.x) - min_line_points + 1:\n",
    "        left = i\n",
    "        line = choose_seed(coordinates, left)\n",
    "        if line is not None:\n",
    "            right = left + seed_seg_points - 1\n",
    "            # grow right\n",
    "            while (right + 1 <= len(coordinates.x) - 1) and \\\n",
    "                  (comp_dist_ptl(coordinates.x[right + 1], coordinates.y[right + 1], line) < ortho_threshold):\n",
    "                right += 1\n",
    "                line = fit_line(coordinates, left, right)\n",
    "            # grow left\n",
    "            while (left - 1 >= 0) and \\\n",
    "                  (comp_dist_ptl(coordinates.x[left - 1], coordinates.y[left - 1], line) < ortho_threshold):\n",
    "                left -= 1\n",
    "                line = fit_line(coordinates, left, right)\n",
    "            # check min_line_points\n",
    "            if right - left + 1 < min_line_points:\n",
    "                i += 1\n",
    "                continue\n",
    "            else: \n",
    "                extracted_lines.append(line)\n",
    "                # start seed checking from the the right next point\n",
    "                i = right + 1\n",
    "        # None means not a seed\n",
    "        else:\n",
    "            i += 1\n",
    "            continue\n",
    "    return extracted_lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Endpoints generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_endpoints(extracted_lines, coordinates):\n",
    "    for line in extracted_lines:\n",
    "        x0_left, y0_left = coordinates.x[line.start], coordinates.y[line.start]\n",
    "        x0_right, y0_right = coordinates.x[line.end], coordinates.y[line.end]\n",
    "        if line.b != 0: \n",
    "            xe_left = (x0_left + line.a * y0_left - line.a * line.c) / (line.a ** 2 + 1)\n",
    "            ye_left = line.a * xe_left + line.c\n",
    "            xe_right = (x0_right + line.a * y0_right - line.a * line.c) / (line.a ** 2 + 1)\n",
    "            ye_right = line.a * xe_right + line.c\n",
    "        else:\n",
    "            xe_left = x0_left\n",
    "            ye_left = line.c/line.a\n",
    "            xe_right = x0_right\n",
    "            ye_right = line.c/line.a\n",
    "        line.leftend = [xe_left, ye_left]\n",
    "        line.rightend = [xe_right, ye_right]\n",
    "    return extracted_lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize grown lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lines_sim = grow_seed(coordinates_sim)\n",
    "display_lines(coordinates_sim, lines_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lines_real = grow_seed(coordinates_real)\n",
    "display_lines(coordinates_real, lines_real)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate endpoints "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "extracted_lines = generate_endpoints(lines_sim , coordinates_sim)\n",
    "display_lines(coordinates_sim, extracted_lines)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "extracted_lines = generate_endpoints(lines_real, coordinates_real)\n",
    "display_lines(coordinates_real, extracted_lines)"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}