Wedge buffer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constructing \"Wedge buffer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "RAD2DEGREE = 180 / math.pi\n",
    "DEGREE2RAD = math.pi / 180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polar_to_cartesian(centre, angle, radius):\n",
    "    x = math.cos(angle) * radius + centre[0]\n",
    "    y = math.sin(angle) * radius + centre[1]\n",
    "    return (x,y)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_arc(centre, radius, rad_from_azimuth, rad_to_azimuth, rad_angle_resolution):\n",
    "    cartesian = []\n",
    "    rad_az = rad_from_azimuth\n",
    "    if rad_from_azimuth < rad_to_azimuth:\n",
    "        while rad_az < rad_to_azimuth:\n",
    "            cartesian.append(polar_to_cartesian(centre, rad_az, radius))\n",
    "            rad_az = rad_az + rad_angle_resolution\n",
    "    else:\n",
    "        while rad_az > rad_to_azimuth:\n",
    "            cartesian.append(polar_to_cartesian(centre, rad_az, radius))\n",
    "            rad_az = rad_az - rad_angle_resolution\n",
    "    cartesian.append(polar_to_cartesian(centre, rad_to_azimuth, radius))\n",
    "    return cartesian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def wedge_buffer(centre, radius, azimuth, opening_angle, inner_radius = 0, angle_resolution = 10):\n",
    "    # make Azimuth 0 north and positive clockwise\n",
    "    azimuth = -1 * azimuth + 90\n",
    "    rad_from_azimuth = (azimuth - opening_angle * 0.5) * DEGREE2RAD\n",
    "    rad_to_azimuth = (azimuth + opening_angle * 0.5) * DEGREE2RAD\n",
    "    rad_angle_res = angle_resolution * DEGREE2RAD\n",
    "    \n",
    "    cartesian_coords = make_arc(centre, radius, rad_from_azimuth, rad_to_azimuth, rad_angle_res)\n",
    "    \n",
    "    if inner_radius <= 0:\n",
    "        cartesian_coords.append(centre)\n",
    "    else:\n",
    "        # Reverse arc at inner radius\n",
    "        cartesian_coords += make_arc(centre, inner_radius, rad_to_azimuth, rad_from_azimuth, rad_angle_res)\n",
    "        \n",
    "    # Close ring\n",
    "    cartesian_coords.append(cartesian_coords[0])\n",
    "    return cartesian_coords"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Demonstrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from shapely.geometry import Polygon, Point, GeometryCollection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib as ml\n",
    "from matplotlib import pyplot\n",
    "# For ipython to display pyplots inline\n",
    "%matplotlib inline\n",
    "# Default figure size\n",
    "pyplot.rcParams['figure.figsize'] = (10.0, 10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simplest case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "centre = (5,10)\n",
    "radius = 1\n",
    "azimuth = 45\n",
    "opening_angle = 120\n",
    "poly = wedge_buffer(centre, radius, azimuth, opening_angle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`poly` is just a list of coordinates forming the polygon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "[(5.965925826289069, 9.74118095489748),\n",
       " (5.996194698091745, 9.912844257252342),\n",
       " (5.996194698091745, 10.087155742747658),\n",
       " (5.965925826289069, 10.258819045102522),\n",
       " (5.90630778703665, 10.4226182617407),\n",
       " (5.819152044288992, 10.573576436351047),\n",
       " (5.707106781186548, 10.707106781186548),\n",
       " (5.573576436351046, 10.819152044288991),\n",
       " (5.422618261740699, 10.90630778703665),\n",
       " (5.258819045102521, 10.965925826289068),\n",
       " (5.087155742747658, 10.996194698091745),\n",
       " (4.912844257252342, 10.996194698091745),\n",
       " (4.741180954897479, 10.965925826289068),\n",
       " (5, 10),\n",
       " (5.965925826289069, 9.74118095489748)]"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using shapely it can be visualized in iPython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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     "execution_count": 131,
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   ],
   "source": [
    "Polygon(poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `inner_radius` will cut away the inner part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   "source": [
    "inner_radius = 0.5\n",
    "poly = wedge_buffer(pnt, radius, azimuth, opening_angle, inner_radius)\n",
    "Polygon(poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`angle_resolution` defines the density of points used to approximate the arc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
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   "outputs": [
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     "execution_count": 133,
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   ],
   "source": [
    "angle_resolution = 20\n",
    "Polygon(wedge_buffer(pnt, radius, azimuth, opening_angle, inner_radius, angle_resolution))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
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     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angle_resolution = 5\n",
    "Polygon(wedge_buffer(pnt, radius, azimuth, opening_angle, inner_radius, angle_resolution))"
   ]
  }
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