02_Visualization_and_Shapes.ipynb

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    "<a href=\"https://colab.research.google.com/github/bwsi-hadr/02-visualization-and-GIS/blob/master/02_Visualization_and_Shapes.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    "# Plotting and GIS in python\n",
    "In this lesson we're going to look at how to present data visually. Visualization is a key part of the analysis workflow. It can reveal insights about data, and its relationships to other variables. It is also an integral tool for communicating data and ideas.\n",
    "\n",
    "We will cover tools for plotting graphs (line, scatter, bar charts, etc), as well as maps (GIS) in this lecture.\n"
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    "# Plotting with matplotlib\n",
    "\n",
    "Matplotlib is the most widely used package for scientific visualization in python. It has a lot of features, but the documentation can be confusing, and the default styles aren't particularly attractive. Nevertheless, knowing how to use matplotlib is fundamental for data science with python. "
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   "source": [
    "import matplotlib as mpl\n",
    "from matplotlib import pyplot as plt #pyplot is a subpackage of matplotlib, and provides the interface that we'll use to create plots\n",
    "plt.style.use('seaborn-whitegrid') # set default visual appearance\n",
    "import numpy as np"
   ]
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    "## Matplotlib conventions\n",
    "There are (confusingly) two different ways to do most things in matplotlib. \n",
    "\n",
    "The first is the MATLAB style interface, which functions as a state machine. Commands are run on a global scope and affect the _current_ figure or axis that you're working on. This is convenient for quick plotting without worrying about the fine-grained details of the plot.\n",
    "\n",
    "The second is the object-oriented interface, which is more \"pythonic\". Figures and axes are _objects_ which have methods and attributes associated with them for plotting and adjusting their appearance. This provides finer-grained control over the plots.\n",
    "\n",
    "It's possible to mix and match between the two interfaces, which can cause confusion for new coders trying to learn how matplotlib works. Just remember there are two ways to do most plotting tasks in matplotlib, so if you see things done differently, that's probably the reason.\n",
    "\n",
    "For this course, we will primarily be using the object-oriented interface, since it aligns better with most of the course material."
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    "## Figures and axes\n",
    "A `Figure` object is a canvas that can hold one or more `Axes` objects. `Axes` are objects which hold the actual plots. (Think of the `Figure` as a piece of paper, and the `Axes` as the actual illustration)"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes([0,0,1,1]) # arguments are location of [left, bottom, width, height], where the units are fraction of the figure\n",
    "x_data = np.arange(0,10,0.5) # points evenly spaced between 0 and 10 with interval of 0.5\n",
    "y_data = 3*x_data + 2 + 0.8*np.random.randn(len(x_data)) # linear + random noise\n",
    "ax.plot(x_data, y_data, marker='o') # 'o' = circle marker; points are marked by circles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A full list of markers is available [here](https://matplotlib.org/3.2.2/api/markers_api.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cclx1plhLDAN"
   },
   "source": [
    "### Subplots\n",
    "Sometimes you want to add multiple plots on the same figure. You can use the `.add_subplot(nrows, ncols, idx)` function of `Figure` to do so.\n",
    "\n",
    "Subplots are set up in a grid, determined by the arguments `nrows, ncols` of the `.add_subplot` function; the `idx` argument determines the location of the created subplot.\n",
    "\n",
    "For example, `fig.add_subplot(2,2,3)` creates a 2 $\\times$ 2 grid, and the idx value of 3 refers to the bottom left grid element.\n",
    "```\n",
    "1 2\n",
    "3 4\n",
    "```\n",
    "\n",
    "In general the indexing convention is left to right on each line:\n",
    "\n",
    "```\n",
    "1 2 ... ncols\n",
    "ncols+1 ... \n",
    "2*ncols+1 ...\n",
    "...\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 369
    },
    "colab_type": "code",
    "id": "TdoX3zebJMb3",
    "outputId": "6ec68286-011d-4235-b96c-2083d8e538d0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=[10,5]) #figure size, in inches\n",
    "ax1 = fig.add_subplot(2,2,1) # \n",
    "ax2 = fig.add_subplot(2,2,3)\n",
    "ax3 = fig.add_subplot(1,2,2) # subplots don't all have to be on the same grid\n",
    "\n",
    "x_data = np.linspace(1,10,100)\n",
    "ax1.plot([0,2], [1,5]) # simply plots a line from (0,1) to (2,5)\n",
    "ax2.plot(x_data, np.sin(x_data))\n",
    "ax3.plot(x_data, x_data**2)\n",
    "\n",
    "# label each one\n",
    "ax1.set_title('This is ax1') # sets a title on ax1\n",
    "ax2.set_title('This is ax2')\n",
    "ax2.set_xlabel('x') # set xlabel\n",
    "ax2.set_ylabel('sin(x)') # set ylabel\n",
    "\n",
    "# it can be more convenient to set all of the labels and limits at once\n",
    "ax3.set(xlim=(0, 10), ylim=(0, 100),\n",
    "       xlabel='x', ylabel='$x^2$',\n",
    "       title='This is ax3'); # encase math in $$ to render exponentiation and other math notation\n",
    "\n",
    "fig.tight_layout() # a function to clean up the spacing between subplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0HG4jcIcPUry"
   },
   "source": [
    "### Appearance\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 262
    },
    "colab_type": "code",
    "id": "6AJCKIqzKzdn",
    "outputId": "8f68f6fd-966a-4b75-f0d1-cd1f154fa4c5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Change colors of lines\n",
    "fig = plt.figure(figsize=[8,4])\n",
    "ax = fig.add_subplot(1,1,1) # create an axis that covers the whole figure\n",
    "x = np.linspace(-5,5,100)\n",
    "ax.plot(x, np.sin(x - 0), color='black')       # specify color by name\n",
    "ax.plot(x, np.sin(x - 1), color='g')           # short color code (rgbcmyk)\n",
    "ax.plot(x, np.sin(x - 2), color='0.5')         # Grayscale between 0 and 1\n",
    "ax.plot(x, np.sin(x - 3), color='#00DDFF')     # Hex code (RRGGBB from 00 to FF) with FF being max and 00 being min\n",
    "ax.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple, values 0 to 1\n",
    "ax.plot(x, np.sin(x - 5), color='chartreuse'); # all HTML color names supported"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 371
    },
    "colab_type": "code",
    "id": "x2eVLMdNK-u-",
    "outputId": "d3f0a7af-0726-44a8-beab-c018cefd6095"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Change linestyle\n",
    "fig = plt.figure(figsize=[8,6])\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.plot(x, x + 0, linestyle='solid')\n",
    "ax.plot(x, x + 1, linestyle='dashed')\n",
    "ax.plot(x, x + 2, linestyle='dashdot')\n",
    "ax.plot(x, x + 3, linestyle='dotted');\n",
    "\n",
    "# For short, you can use the following codes:\n",
    "ax.plot(x, x + 4, linestyle='-')  # solid\n",
    "ax.plot(x, x + 5, linestyle='--') # dashed\n",
    "ax.plot(x, x + 6, linestyle='-.') # dashdot\n",
    "ax.plot(x, x + 7, linestyle=':'); # dotted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ii-BW0S6tpe_"
   },
   "source": [
    "There are also [bar charts](https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.bar.html#matplotlib.pyplot.bar), [pie charts](https://matplotlib.org/3.1.1/gallery/pie_and_polar_charts/nested_pie.html#sphx-glr-gallery-pie-and-polar-charts-nested-pie-py), and [many other tutorials in the matplotlib documentation](https://matplotlib.org/3.1.1/tutorials/introductory/sample_plots.html#sphx-glr-tutorials-introductory-sample-plots-py). Check them out for inspiration!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ahcW_XmxvA-2"
   },
   "source": [
    "## Exercise\n",
    "Using any data that you looked at earlier this week, make a plot that visualizes some element of your analysis. We'll ask a few people to present their results when they're ready.\n",
    "\n",
    "Matplotlib can take numpy arrays or pandas series and dataframes as inputs. In addition, pandas dataframes have [a built-in interface to automatically call matplotlib functions](https://pandas.pydata.org/pandas-docs/stable/user_guide/visualization.html). This can be a convenient way to visualize for exploratory analysis. However, it's less customizable, so it may not be suitable for making presentation-quality graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LPYOcEpswPhF"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OLu4MBP69q6T"
   },
   "source": [
    "# Shapes and Geometry\n",
    "\n",
    "For geospatial data analysis, we will be dealing with a lot of geometry. The library that we will be using for geometry is called Shapely.\n",
    "\n",
    "Shapely is a _planar geometry_ package. Meaning that it is concerned with 2Dgeometry, making it well suited for representing and analyzing information on maps.\n",
    "\n",
    "This content is based off of the [Automating GIS Processes course](https://automating-gis-processes.github.io/2018/) from the University of Helsinki."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "eGxA0wEJQPEs"
   },
   "outputs": [],
   "source": [
    "import shapely\n",
    "from matplotlib import pyplot as plt\n",
    "from shapely.geometry import Point, LineString, Polygon\n",
    "from descartes import PolygonPatch # will be used to visualize polygons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Z2eO3jRJSf0x"
   },
   "source": [
    "## Shapely objects\n",
    "Shapely is a library for representing geometric objects, such as points, lines, and polygons. \n",
    "\n",
    "The primary classes in Shapely are the `Point`, `LineString`, and `Polygon` classes. Each are represented using 2 or 3-dimensional coordinate tuples (x,y(,z)).\n",
    "\n",
    "- The `Point` object represents a single point in space. Points can be either two-dimensional (x, y) or three dimensional (x, y, z).\n",
    "- The `LineString` object (i.e. a line) represents a sequence of points joined together to form a line. Hence, a line consists of a list of at least two coordinate tuples.\n",
    "- The `Polygon` object represents a filled area that consists of a list of at least three coordinate tuples that forms the outerior ring and a (possible) list of hole polygons.\n",
    "\n",
    "There are also collections of objects, aptly named `MultiPoint`, `MultiLineString`, and `MultiPolygon`. These are, as their names suggest, collections of multiple `Point`, `LineString`, and `Polygon` objects respectively. There also exists a broader class of `GeometryCollection`, which can include objects of any geometry type.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kW6HjI5mVZrt"
   },
   "source": [
    "## `Point` objects\n",
    "\n",
    "`Points` require a tuple (2 for 2D, 3 for 3D) to specify their location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 69
    },
    "colab_type": "code",
    "id": "aTfLuqlFVkWF",
    "outputId": "248f3fd9-06ce-4e7a-e431-76f4623f24d1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "POINT (2.2 4.2)\n",
      "POINT Z (9.26 -2.456 0.57)\n",
      "<class 'shapely.geometry.point.Point'>\n"
     ]
    }
   ],
   "source": [
    "# Create Point geometric object(s) with coordinates\n",
    "point1 = Point(2.2, 4.2)\n",
    "point2 = Point(7.2, -25.1)\n",
    "point3 = Point(9.26, -2.456)\n",
    "point3D = Point(9.26, -2.456, 0.57)\n",
    "point3D2 = Point(9.26, -2.456, 0)\n",
    "\n",
    "# What is the type of the point?\n",
    "point_type = type(point1)\n",
    "\n",
    "# Let's examine the objects\n",
    "print(point1)\n",
    "print(point3D)\n",
    "print(type(point1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WAG3BuauWloM"
   },
   "source": [
    "We can see that the type of the point is shapely's `Point` which is represented in a specific format that is based on [GEOS C++ library](https://trac.osgeo.org/geos), which is one of the standard libraries in GIS. 3D-point can be recognized from the capital '`Z`' in front of the coordinates (signifying that there's a 'z' element in the (x,y,z) tuple)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "K0Og713eXLuf"
   },
   "source": [
    "### `Point` class attributes and functions\n",
    "`Point` objects have some built-in attributes and functions. One of the most useful ones are the ability to extract the coordinates of a Point and calculate the Euclidean distance between points.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "colab_type": "code",
    "id": "InP-kYL6WZQn",
    "outputId": "46b51b3e-b1c0-41e5-ef3c-560c37f79e2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "shapely.coords.CoordinateSequence"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the coordinates\n",
    "point_coords = point1.coords\n",
    "\n",
    "# What is the type of this?\n",
    "type(point_coords)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 167
    },
    "colab_type": "code",
    "id": "nmGyLHzfW2MK",
    "outputId": "6d760ac0-f224-4224-a8b5-e25ac6b92744"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xy variable:\n",
      " (array('d', [2.2]), array('d', [4.2])) \n",
      "\n",
      "x variable:\n",
      " 2.2 \n",
      "\n",
      "y variable:\n",
      " 4.2\n"
     ]
    }
   ],
   "source": [
    "# Get x and y coordinates\n",
    "xy = point_coords.xy\n",
    "\n",
    "# Get only x coordinates of Point1\n",
    "x = point1.x\n",
    "\n",
    "# Whatabout y coordinate?\n",
    "y = point1.y\n",
    "\n",
    "# Print out\n",
    "print(\"xy variable:\\n\", xy, \"\\n\")\n",
    "print(\"x variable:\\n\", x, \"\\n\")\n",
    "print(\"y variable:\\n\", y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "colab_type": "code",
    "id": "85yXDkIOfw_Z",
    "outputId": "3ea941e6-8525-4e74-e7cd-add386c251f9"
   },
   "source": [
    "# Calculate the distance between point1 and point2\n",
    "point_dist = point1.distance(point2)\n",
    "\n",
    "print(\"Distance between the points is {0:.2f} decimal degrees\".format(point_dist))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "colab_type": "code",
    "id": "sFCBm41Pf0Rs",
    "outputId": "9f999d35-7796-4ee9-8f60-995e8bb69d0f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.723559679150142"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.sqrt((2.2-7.2)**2 + (4.2+25.1)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KKyze6mDgSv-"
   },
   "source": [
    "Note that shapely is planar geometry library, and thus only considers the planar (x,y) coordinates when computing distance. \n",
    "Even though `point3D` and `point3D2` have differing `Z` coordinates, they return a planar distance of zero. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 73
    },
    "colab_type": "code",
    "id": "6mblpggBgK44",
    "outputId": "d4ef4e0d-5964-4ffb-ee4a-580c5fe665d7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "POINT Z (9.26 -2.456 0.57)\n",
      "POINT Z (9.26 -2.456 0)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(point3D)\n",
    "print(point3D2)\n",
    "point3D.distance(point3D2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Let's put the `distance` function into action. Write a function that takes in a list of points and calculates the distance between the two closest points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getClosestDist(points_list):\n",
    "  \"\"\"\n",
    "  input: points_list, list of Points - a list of shapely Point objects\n",
    "  output: dist, float - the distance between the two closest points in points_list\n",
    "  \"\"\"\n",
    "  # fill this in with your code\n",
    "  all_dist = []\n",
    "  combos = itertools.combinations(points_list, 2)\n",
    "  for combo in combos:\n",
    "    all_dist.append(combos[0].distance(combos[1]))\n",
    "  return min(all_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DVtosdJKmaeS"
   },
   "source": [
    "## LineString Objects\n",
    "A `LineString` is a sequence of connected line segments. One can be constructed from a list of shapely `Point` objects, or from a list of tuples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "id": "HGsQDXWpmy51",
    "outputId": "4bdfac59-9d27-4326-bfa0-7cba68003e00"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "line variable: \n",
      " LINESTRING (2.2 4.2, 7.2 -25.1, 9.26 -2.456) \n",
      "\n",
      "line2 variable: \n",
      " LINESTRING (2.2 4.2, 7.2 -25.1, 9.26 -2.456) \n",
      "\n",
      "is line equal to line2:  True \n",
      "\n",
      "type of the line: \n",
      " <class 'shapely.geometry.linestring.LineString'>\n"
     ]
    }
   ],
   "source": [
    "# Create a LineString from our Point objects\n",
    "line = LineString([point1, point2, point3])\n",
    "\n",
    "# It is also possible to use coordinate tuples having the same outcome\n",
    "line2 = LineString([(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)])\n",
    "\n",
    "# Print the results\n",
    "print(\"line variable: \\n\", line, \"\\n\")\n",
    "print(\"line2 variable: \\n\", line2, \"\\n\")\n",
    "print(\"is line equal to line2: \", line==line2, \"\\n\")\n",
    "print(\"type of the line: \\n\", type(line))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YHC2sjAunZxG"
   },
   "source": [
    "### `LineString` class attributes and functions\n",
    "`LineString` objects have many useful built-in attributes and functionalities. \n",
    "\n",
    "It is, for instance, possible to extract the coordinates or the length of a LineString (line), calculate the centroid of the line, create points along the line at specific distance, calculate the closest distance from a line to specified `Point` and simplify the geometry. See full list of functionalities from [Shapely documentation](https://shapely.readthedocs.io/en/latest/manual.html#geometric-objects). \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 92
    },
    "colab_type": "code",
    "id": "-taIq5GEnIPL",
    "outputId": "f6bab6e6-0644-4360-cfad-3e349729b511"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)]\n",
      "lxy= (array('d', [2.2, 7.2, 9.26]), array('d', [4.2, -25.1, -2.456]))\n",
      "x coordinates:  array('d', [2.2, 7.2, 9.26])\n",
      "y coordinates:  array('d', [4.2, -25.1, -2.456])\n"
     ]
    }
   ],
   "source": [
    "# Get list of coordinates\n",
    "print(list(line.coords))\n",
    "\n",
    "# Get x and y elements of the line separately (useful for plotting)\n",
    "lxy = line.xy\n",
    "print('lxy=',lxy)\n",
    "\n",
    "# we can separate the outputs into the x and y variables respectively\n",
    "line_x, line_y = lxy\n",
    "print('x coordinates: ', line_x)\n",
    "print('y coordinates: ', line_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AZhrAcKzrJD8"
   },
   "source": [
    "We can use matplotlib to plot this `LineString`\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "m0V5wtSgpZeE",
    "outputId": "8cfa8e16-7d16-4a2a-9161-bb77aa1768f1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f681b761e90>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.plot(line_x, line_y, 'b-') # draw as blue line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "y3A7ebQAr-Jh"
   },
   "source": [
    "There are also many useful attributes of the linestring that we can get automatically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 73
    },
    "colab_type": "code",
    "id": "sq2L37kMrgQE",
    "outputId": "0e9cf2bd-3edb-4609-c2e4-d40159b4085b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of our line: 52.46\n",
      "Centroid of our line:  POINT (6.229961354035622 -11.89241115757239)\n",
      "Type of the centroid: <class 'shapely.geometry.point.Point'>\n"
     ]
    }
   ],
   "source": [
    "# Get the length of the line\n",
    "l_length = line.length\n",
    "print(\"Length of our line: {0:.2f}\".format(l_length)) # the {0:.2f} notation is a special placeholder for the .format() string function. \n",
    "# the curly brackets {} indicate that this should be filled with a variable value. The initial {0} indicates that it should be filled with the first argument of .format()\n",
    "# the {:.2f} part of the placeholder indicates the formatting. The colon specifies that it is a formatting string, and .2f indicates that it should have 2 digits after the decimal point\n",
    "# f indicates that it should be numeric (float)\n",
    "\n",
    "# Get the centroid of all the points in the linestring\n",
    "l_centroid = line.centroid\n",
    "print(\"Centroid of our line: \", l_centroid)\n",
    "\n",
    "# the centroid is a Point type object\n",
    "centroid_type = type(l_centroid)\n",
    "print(\"Type of the centroid:\", centroid_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1a2MaC_Vv5lq"
   },
   "source": [
    "We can plot the location of the centroid (average location of all points, equally weighted)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "ld7FJUcAsIv-",
    "outputId": "36873ac1-23ae-419d-ed52-e3195e34aca9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f681b6da750>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_centroid_x, l_centroid_y = l_centroid.xy\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.plot(line_x, line_y, 'b-') # draw as blue line\n",
    "ax.plot(l_centroid_x, l_centroid_y, 'ro', markersize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AGKuTQ9zwGeK"
   },
   "source": [
    "### Exercise: Compute and plot midpoint of a LineString\n",
    "The centroid gives the arithmetic average of all of the points in the LineString. However, it is also useful to know where the midpoint of a LineString is. That is, if you were traveling along the LineString from one end to the other, at which point would the distance you've traveled be equal to the distance you have yet to travel.\n",
    "\n",
    "For this exercise, write a function which takes any valid `LineString` object as an input, outputs the coordinates of the midpoint, and draws a plot of both the LineString and midpoint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OUSl-3wEtPKp"
   },
   "outputs": [],
   "source": [
    "def getMidpoint(line):\n",
    "  \"\"\"\n",
    "  input: line, LineString - any valid shapely LineString object\n",
    "  output: midpoint, Point - a shapely Point object corresponding to the midpoint of the input LineString\n",
    "  Also plot the input LineString as well as the midpoint\n",
    "  \"\"\"\n",
    "  # fill this in with your code\n",
    "  dist_x = []\n",
    "  dist_y = []\n",
    "  i = 0\n",
    "  while i < (len(line.coords) - 1):\n",
    "    new_forecasts.append(MultiPolygon([all_forecasts[i], all_forecasts[i + 1]]).convex_hull)\n",
    "    dist_x.append(line.coords[i+1][0] - line.coords[i][0])\n",
    "    dist_y.append(line.coords[i+1][1] - line.coords[i][1])\n",
    "    i += 1    \n",
    "  l_length = line.length\n",
    "  mid_x = sum(dist_x)\n",
    "  midpoint = Point(mid_x, mid_y)\n",
    "  return midpoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IvjUoAh0hZQL"
   },
   "source": [
    "_Note there is an `interpolate` method in shapely that makes this trivial. Try to do it without using it. You can use `interpolate` to check your work._ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, generalize your function such that it takes both a `LineString` object and a floating-point value `d` and outputs the \"interpolation point\": the point that is exactly `d` of the way on the `LineString`. In other words, the interpolation point is the point you would be at if you were to travel `d` * (length of the `LineString`) along the `LineString`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getInterpolation(line, d):\n",
    "    \"\"\"\n",
    "    input: line, LineString - any valid shapely LineString object\n",
    "           d, float (0.0 <= d <= 1.0) - the fraction along the line to interpolate\n",
    "    output: interpolationPoint, Point - a shapely Point object corresponding to the midpoint of the input LineString\n",
    "    Also plot the input LineString as well as the interplation point\n",
    "    \"\"\"\n",
    "    # fill this in with your code   \n",
    "    mid = line.length / 2\n",
    "    interpolationPoint = line.interpolate(mid)\n",
    "    \n",
    "    lxy = line.xy\n",
    "    line_x, line_y = lxy\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(1,1,1)\n",
    "    ax.plot(line_x, line_y, 'b-') # draw as blue line\n",
    "    ax.plot(interpolationPoint.x, interpolationPoint.y, 'ro', markersize=10)\n",
    "    \n",
    "    return interpolationPoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"5.612414738988585 -22.656750370473112 2.0 2.0\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-43.313500740946225)\"><circle cx=\"6.612414738988585\" cy=\"-21.656750370473112\" r=\"0.06\" stroke=\"#555555\" stroke-width=\"0.02\" fill=\"#66cc99\" opacity=\"0.6\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.point.Point at 0x7f681b6144d0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "getInterpolation(LineString([(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)]), 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    ".interpolate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Again, try to do this without using the `interpolate` method. In fact, what you are doing here is essentially implementing Shapely's `interpolate` method._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IX6aH-y0xfMC"
   },
   "source": [
    "## Polygon object\n",
    "\n",
    "Creating a `Polygon` object continues the same logic of how `Point` and `LineString` were created, but the `Polygon` object accepts only coordinate-tuples as input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 54
    },
    "colab_type": "code",
    "id": "Niv6azGoSR39",
    "outputId": "37175bd2-9c10-4563-bae4-d1cccedf859b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coords from point objects are: [(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)]\n",
      "poly and poly2 are equal:  True\n"
     ]
    }
   ],
   "source": [
    "# Create a Polygon from coordinates\n",
    "poly = Polygon([(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)])\n",
    "\n",
    "# We can also use our previously created Point objects (same outcome)\n",
    "# --> notice that Polygon object requires x,y coordinates as input\n",
    "poly2_coords = [(p.x, p.y) for p in [point1, point2, point3]]# using list comprehension to generate a list of coordinates\n",
    "print('coords from point objects are:', poly2_coords)\n",
    "poly2 = Polygon(poly2_coords) \n",
    "print('poly and poly2 are equal: ', poly == poly2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HLs1PwlAZDe7"
   },
   "outputs": [],
   "source": [
    "# there are some useful attributes and functions:\n",
    "x_min, y_min, x_max, y_max = poly.bounds # gives a tuple with the coordinates of a bounding rectangle: (x_min, y_min, x_max, y_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "GOnrnxMYSaUD",
    "outputId": "8e1cfccf-93f8-43b7-9cd4-cc11f9943769"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a polygon\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "patch = PolygonPatch(poly2, fc='#FF6600', ec='black', alpha=0.8, linewidth=2) # arguments are PolygonPatch(shapely_polygon, fc=face_color, ec=edge_color, alpha=transparency, **kwargs)\n",
    "# PolygonPatch creates a matplotlib object, so the matplotlib kwargs will work in general to modify it\n",
    "ax.add_patch(patch) # puts the patch object on the axes\n",
    "ax.set(xlim=[x_min, x_max],ylim=[y_min,y_max]) # set limits at bounding polygon coordinates\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ixMmftPZV4rT"
   },
   "source": [
    "Polygon objects can have holes in them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ilw7HJgcV3sX"
   },
   "outputs": [],
   "source": [
    "\n",
    "# Let's create a big rectangle and put some holes in it\n",
    "\n",
    "# First we define our exterior\n",
    "poly_exterior = [(-180, 90), (-180, -90), (180, -90), (180, 90)]\n",
    "\n",
    "# Let's first create a single big hole \n",
    "# each hole is a list of coordinates.\n",
    "single_hole = [[(170, 80), (170, -80), (-170, -80), (-170, 80)]]\n",
    "# There can actually be multiple holes, so the holes should be lists of lists\n",
    "# hence the double square brackets [[]] for single_hole and double_hole\n",
    "double_hole = [[(100, 80), (100, -80), (-10, -20), (-10, 20)],[(-20, 30),(-125, -45),(-120, 40)]]\n",
    "\n",
    "# polygon without a hole\n",
    "poly_no_holes = Polygon(shell=poly_exterior)\n",
    "\n",
    "# polygons with holes\n",
    "poly_with_a_hole = Polygon(shell=poly_exterior, holes=single_hole)\n",
    "poly_with_holes = Polygon(shell=poly_exterior, holes=double_hole)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "mU044pp6n0qJ",
    "outputId": "20a06ad3-301b-4027-84d4-4230195edc89"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-95.0, 95.0), (-185.0, 185.0)]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(311)\n",
    "patch1 = PolygonPatch(poly_no_holes,fc='#1155FF',alpha=0.5)\n",
    "ax1.add_patch(patch1)\n",
    "ax1.set(xlim=[-185,185], ylim=[-95,95])\n",
    "\n",
    "ax2 = fig.add_subplot(312)\n",
    "patch2 = PolygonPatch(poly_with_a_hole,fc='#1155FF', ec='#FFFFFF',alpha=0.5)\n",
    "ax2.add_patch(patch2)\n",
    "ax2.set(xlim=[-185,185], ylim=[-95,95])\n",
    "\n",
    "ax3 = fig.add_subplot(313)\n",
    "patch3 = PolygonPatch(poly_with_holes,fc='#1155FF', ec='#FFFFFF',alpha=0.5)\n",
    "ax3.add_patch(patch3)\n",
    "ax3.set(xlim=[-185,185], ylim=[-95,95])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gDR2tiINsC3e"
   },
   "source": [
    "Note there are some constraints about the location of holes within polygons (what's allowed and not allowed). See [the shapely manual](https://shapely.readthedocs.io/en/latest/manual.html#polygons) for details.\n",
    "\n",
    "Also note that the order of the points which define a hole/polygon matter: If the polygon exterior points are listed counter-clockwise, then the hole should be clockwise (and vice versa). If you don't want to bother dealing with this, you can call\n",
    "```\n",
    "polygon_with_holes = shapely.geometry.polygon.orient(polygon_with_holes)\n",
    "```\n",
    "to orient it automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "tio0HuRGsBlg",
    "outputId": "48f48a83-d076-46b8-f841-a2a51a54c4d4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-95.0, 95.0), (-185.0, 185.0)]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's try with the hole oriented incorrectly\n",
    "single_hole_backwards = [single_hole[0][::-1]] # [::-1] reverses the order of single_hole[0] (we have to use [0] because single_hole is a list of lists)\n",
    "# recall that the indexing notation `listname[idx_a:idx_b]` is shorthand for \"get elements of listname starting at idx_a, going up to (but not including) idx_b\"\n",
    "# Omitting `idx_a` means \"start at beginning\"; omitting `idx_b` means \"go until the end\"\n",
    "# furthermore, you can use `listname[idx_a:idx_b:step_size]` to get every \"step_size\"-th element\n",
    "# thus, the index [::-1] means \"all elements, but counting backwards by 1\"\n",
    "poly_with_bkw_hole = Polygon(shell=poly_exterior, holes=single_hole_backwards)\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "patch1 = PolygonPatch(poly_with_bkw_hole,fc='#1155FF',alpha=0.5)\n",
    "ax1.add_patch(patch1)\n",
    "ax1.set(xlim=[-185,185], ylim=[-95,95])\n",
    "# note that the hole is filled incorrectly (not actually a hole!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "colab_type": "code",
    "id": "Npd2eSvUuzdS",
    "outputId": "ac7a4e2c-2895-4bf0-ef81-80b9ac4aebff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-95.0, 95.0), (-185.0, 185.0)]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fix it\n",
    "poly_with_bkw_hole = shapely.geometry.polygon.orient(poly_with_bkw_hole) # fix the orientation\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "patch1 = PolygonPatch(poly_with_bkw_hole,fc='#1155FF',alpha=0.5)\n",
    "ax1.add_patch(patch1)\n",
    "ax1.set(xlim=[-185,185], ylim=[-95,95])\n",
    "# all better!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EvTOT7RfuyAG"
   },
   "source": [
    "There are many functions associated with shapely objects which can help you create new shapes and do spatial analyses. We will go over a few of them, but you can check them all out in the [shapely manual](https://shapely.readthedocs.io/en/latest/manual.html#spatial-analysis-methods).\n",
    "\n",
    "`object.buffer(distance)` creates an object that encompasses all of the space `distance` beyond the current boundaries of `object`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "id": "KeCOsm0toMDK",
    "outputId": "4dbe2577-e0f7-462e-db5f-ce69655fc24a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd9fc08b2d0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "patch1 = PolygonPatch(poly_with_holes,fc='#0000FF',alpha=1)\n",
    "poly_with_buffer = poly_with_holes.buffer(10)\n",
    "patch2 = PolygonPatch(poly_with_buffer,fc='#0055FF',alpha=0.5)\n",
    "p1 = ax1.add_patch(patch1)\n",
    "p2 = ax1.add_patch(patch2)\n",
    "ax1.set(xlim=[-200,200], ylim=[-110,110])\n",
    "ax1.legend({'original polygon':p1, 'buffered':p2},loc='best')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff832e10>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "current_location = Point((0, 0))\n",
    "area_within_1km = current_location.buffer(1)\n",
    "area_within_1km"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "oCbxEaOTe5Kv",
    "outputId": "afe9c934-a726-4bf0-d707-5d64bbf4cbb3"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-9.8 -9.8 21.6 21.6\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,2.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.43200000000000005\" opacity=\"0.6\" d=\"M 11.0,1.0 L 10.95184726672197,0.019828596704394963 L 10.807852804032306,-0.9509032201612808 L 10.56940335732209,-1.902846772544621 L 10.23879532511287,-2.826834323650894 L 9.819212643483553,-3.713967368259972 L 9.314696123025456,-4.555702330196017 L 8.730104533627374,-5.343932841636449 L 8.07106781186548,-6.071067811865469 L 7.343932841636462,-6.7301045336273635 L 6.555702330196031,-7.314696123025447 L 5.713967368259986,-7.819212643483546 L 4.826834323650909,-8.238795325112862 L 3.902846772544636,-8.569403357322084 L 2.9509032201612966,-8.807852804032303 L 1.9801714032956208,-8.951847266721966 L 1.0000000000000162,-9.0 L 0.019828596704411172,-8.95184726672197 L -0.9509032201612646,-8.807852804032308 L -1.902846772544605,-8.569403357322093 L -2.8268343236508784,-8.238795325112875 L -3.713967368259957,-7.81921264348356 L -4.555702330196005,-7.314696123025463 L -5.343932841636439,-6.730104533627382 L -6.071067811865462,-6.071067811865488 L -6.730104533627359,-5.343932841636468 L -7.314696123025444,-4.555702330196036 L -7.819212643483542,-3.71396736825999 L -8.238795325112862,-2.8268343236509113 L -8.569403357322084,-1.9028467725446365 L -8.807852804032303,-0.9509032201612948 L -8.951847266721968,0.01982859670438286 L -9.0,0.9999999999999899 L -8.95184726672197,1.980171403295597 L -8.807852804032306,2.9509032201612753 L -8.569403357322091,3.902846772544617 L -8.23879532511287,4.826834323650893 L -7.819212643483553,5.713967368259972 L -7.314696123025454,6.55570233019602 L -6.730104533627371,7.343932841636453 L -6.071067811865477,8.071067811865476 L -5.343932841636459,8.730104533627367 L -4.55570233019603,9.314696123025447 L -3.713967368259987,9.819212643483546 L -2.8268343236509117,10.238795325112862 L -1.902846772544641,10.569403357322084 L -0.9509032201613041,10.8078528040323 L 0.019828596704368984,10.951847266721966 L 0.9999999999999715,11.0 L 1.9801714032955742,10.951847266721972 L 2.950903220161248,10.807852804032311 L 3.902846772544587,10.569403357322098 L 4.826834323650859,10.238795325112884 L 5.713967368259937,9.81921264348357 L 6.555702330195982,9.31469612302548 L 7.3439328416364145,8.730104533627403 L 8.071067811865436,8.071067811865515 L 8.730104533627333,7.343932841636501 L 9.314696123025417,6.555702330196074 L 9.81921264348352,5.713967368260034 L 10.238795325112841,4.826834323650962 L 10.569403357322066,3.9028467725446925 L 10.80785280403229,2.950903220161357 L 10.95184726672196,1.9801714032956848 L 11.0,1.0000000000000824 L 11.0,1.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff792e90>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you can create a circle using a point and buffer\n",
    "Point(1,1).buffer(10) # creates a point centered at 1,1 with radius 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "id": "QTVO1v50d49y",
    "outputId": "6b281e9d-09ea-4c2a-e568-1028b365f322"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7feeff9ff150>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LGr6+k9Drv2HFiiU8+uijrg5TFCOS/IUowVItmTy9fy2bzx/HaFsGODvJ6nO02vH06/cwb799hMDAQFeGKYohSf5ClECKovDpuVie3Lcas60fWfbPAGcmWV1Eq51A+fIHWbduLe3atXN1qKKYkuQvRAlz3nSV4b+t5JfLVzDYvgBaOtGLgkq1Ej+/yYwdO5JXX12NVqt1daiiGJPkL0QJYVfs/O/UTl48+AlZ9vFYlen8uyKWY06h14+mSpWrrF+/NXcdLlG2SPIXogT4M+MCg2M/5Fi6FwbbT0ADJ3qxoVa/ja/vfKZNm8xLLz2Hl5ekgLJKfvNCFGNWu42Fx79i3vGvybLNwM4zgDOzaw+h1z9J/frlWLt2D7Vq1XJ1qKKEkeQvRDF1IPU0A/Ys46ypKibbfsCZ2bVmvL1fxcfnA/773wU89dRImawlAEn+QhQ7JpuFaYc/5f1TP2KyvQEMw7nJWj+j1z9F69ZRfPTRQSpVquTiSEVJJslfiGJk16WjDI5dTmr2A5hsRwFnZtem4+s7Ba32M5YvX0yfPn1cHaYoBST5C1EMpFkMPPP7Oj49ewSjbSnQ08mevkanG0vPnl1YsuQo5cuXd2WYohSR5C9EEfv83F5G/LYKk+0xzPaNgDOza1Pw85tAUNBvrFmzgk6dOrk6TFHKuDT5HzlyhKeffppq1aoBUKdOHZ588kkmTZqEzWYjNDSU1157LbfEoxBl2UVzGiN/W8WulAsYbZuAtk70ogBr0GpfpE+fh/ngg8PodDoXRypKI5cmf6PRSLdu3Zg2bVrutilTpjBo0CAeeughFi1axKZNmxg0aJArDytEiaIoCh+d2cWzv39Mlu0pspXZgJ8TPSWg042hYsXzfPzx1+j1ekn8wmEuLeBuMBhu2RYbG5t7CdqpUyd2797tykOWGsnmNL5LPsSnZ/ewI/kwf2ZcwGyzFHVYwsVOZSbT6vv/MPHAL2Rad5KtLKTgid+GWv0OWu29TJ7chvj4fTRr1swd4YpSzOVn/nFxcTz55JOYTCYmTJiAyWTKHeYJDQ0lJSXltm3j4+OdPm5SUhJ2u93p9kVpe/IhJh/azNH0M/hpGqEoQai4io2zmGwX0Gn8ifAL4y5dCHX8g6hVrgKRuhAidSFU04cS4uMvz22XADbFzht/bGHWsc1Y7FOwKc/j3H+/o2i1I7jrLoXXX19N9erVOXnyJABms7lQ/488wW5XijqEYiU+Pr7ISmK6NPnXrVuXcePG0alTJ06fPs3w4cOxWq2531eUO//io6KcqS2a48SJE6jVLr2Icbtsu5XRcavZkHQUo+0/QDRZdu9/7WUnw5pMRmYCf2Ym8t2lBHzUZ/BTHwMSybKfw66YCfENo7I2hFrlKlDXvzzV9Nc/HHQhVNFWwFfz736FJx1KS2DgnuUkGMMw2fYBNZ3oxYKX1wJ8fd9l0aK5jBkz6pa/+fj4+EL9P/IEtVpOVG4UFRVVqOQfFxfndFuXJv+aNWtSs2bOH3b16tUJCQnhwoULmM1m/Pz8SE5OJiwszJWHLJHsip3evy5h5yU9RtsRIOAOe6qBitdfLQCw2HNe/8jkgjmJC+YE9qUmoiYBreY0XqoDWJUkzPZk9JoAKmrDqKarQF3/YGqWC/7n6kEXSrBPObl6cAOzzcKMo5/x7snvMdsWojAS5yZr7UGvf5L776/O6tUHqFKliqtDFWWQS5P/pk2bMBqNDBs2jJSUFK5cuULv3r3ZunUrPXv2ZNu2bbRp08aVhyyR5sd/yc5LVoy2L3DuRt+NygFR119gBwy2G79vI916kfSMRP7ISGBbcgK+6jP4qo8ACdevHiyE+oZTVffP1cPfHw6RuhCq6Crgo5anggvi58vHGbRnOVcsTTDZjpDzAV5Qmfj4TEOr/YQPPniLfv36yYe0cBmX/o/u0qULL774Ilu3bsVisTBr1iyioqKYPHkyGzZsoFKlSjz22GOuPGSJk2S8zPzjX18vrF3YxO8IDVD5+usBALLsOa9/pHPenMR5cwKxVxNRcwad5gwadRxWeyIm2yUCvMtT0S+UavoQ6vqXp+aN9x50IQR56yUxAenZRp77fQPrk/Zjsi0BnJ1duxWdbjQ9erRj6dIjVKhQwZVhCuHa5B8YGMiyZctu2b5ixQpXHqZE+8/xb7DaRwDVijqUGwQA9a+/cq4eMm1A7hWElbTsC6RlJxKfkcC3FxPwU5/BR/07kIjZfhYVdkJ9w6iqC6WmPpiogJuvHiprg/Eu5VcPX1/Yz+N7V2CwdsdsjwecmV17Ba32Ofz9f2L16g/o1q2bq8MUApAZvh5lV+zEJPxCtvJmUYdSQF5A1euvVgCY7Tmvf1zjrCmRs6ZEdl9JQMMZtF6n0aj2YrUnYbKlEOgdTEVtGNV1Fbg7IIia+pCbPiCCfPSe/9Fc4JL5Gk/FxbA9ORGjbR3Q0YleFGADWu1zPP54f1577TDlypVzcaRC/EOSvwcdvpaIQhDOPe1R3AUCDa+/ci4aMq03fj+b1OzzpGYnciw9ka8vnrl+9RAHJGKynUWjUhPmG3b93kMwd/uXp5o+NPfDoZJfebzURfNY3O0oisKaxJ8Yt38dWbYnsCjfAM5MsjqLTjeWsLDTrF//GS1atHB1qELcQpK/Bx25lgQ0Keowiog3OUNd/wx33Xz1oJCtpJFoSiTRlMgvVxLxUp1GqzmNml/JVs5itl2mvE8IFf1Cqa6vwN3+5alRrgLVbrh6CPD2zAzXBEMKQ/d+xP5UMwbbNuBeJ3qxo1J9gJ/fDJ5/fgKvvPKpLH0iPEaSvwddNKdhseX1mF7OpX/OryXy+isMF0/ELqZU5IyRlwcaA2BVIOOmqwcLVyznuGJJ5Eh6Il9eSECrOYWPei92JRGT7RxeKg0RfuE3XT3U8a9Em5C6hPje6ZFax9kUO+/8uZXpRz4jy/4iNmUSOR9sBXUcvf4pata0sX79D9SrV6/QsQlREJL8PSjDasKi3JXHHkn4+DxJ27bdOHMmgYsXEzGZ0tFqq6LRRJKdHYnJFImiRJJzBh1Jzji81hPhFwM+5FSz+qeilcmW88qhYFWucsaYyBljIj9dzrl60Gl+J8v+Ad0imvJm42hqlHNmjXw4ei2JgXuWc8oQhNG2B7jbiV6y8fJahI/Pm7z66kwmTHi6yGZ4irJNkr8HXbFkcecJXQAZhIZG8t13n+ZuMZlMJCUlkZiYSEJCAmfOJPLHHz/z11/rOHs2gatXz+LlFYCvbzXs9kjM5pwPiZwPhr8/IEJxbnJRSaMCKlx/NQVyrh7SrQDpfH3hbXYkzyCm+Uh6Vb7f4V4tditzjn7Bf//chtk2D4XROHc1tg+9fiT33FOJmJi43NVvhSgKkvw9KNWSRc6krDvJRK+/+ftarZY6depQp06d27aw2+1cunQp98MhMTGRvXsPkJLyI4mJiVy8mEBWlgGttipqdbV/XT38/QFRBc/MOShKAdiUVzDYujM49iHWN1fRs/J9+bbac+UEA/cs51JWPUy2w+TMlygoIz4+M/D1jWHJkjcYMmSwzIkQRU6SvwelWbIA/zz2yKBcuby+fyu1Wk1ERAQRERHcf3/O2ey/13gxGAy3XD0cP76LU6cSOX8+kStXzuLjUx4fn0js9mqYTJFYrf++eqhA6bh6uBeT7WsGx3bl2IPVidSF3HavTKuZFw9uYHXCXky2xUA/nPv5d6DTjaJLl+YsW3aE0NDQwgQvhMtI8vegdKuZ/JJ/QEDBkr8j9Ho9devWpW7durf9vs1mIzk5mcTExNwPiBMnTvLnnztJTEwkOTkBi8WMVhuJWh2JxZLzAfHPTem/rx5KypMq95Fln8jTcev4qs0zt3x368XfGbr3IzKyO1+frOXM7NpU/PxeQK/fzqpVS+nRo0ehoxbClST5e1B6dv7JPzDQ9ck/PxqNhkqVKlGpUqU7PmOekZGRe/WQmJjIqVMJ/PHH9tyrh9TU8/j6VsDb+3ZXD39/QJSnuFw9WJWX2HHpHU5lJufeAL6SlcGYuDVsuXgSo20V0NXJ3j9Fq53AoEG9efPNo/j7e/53KkR+JPl7UKbVRH5j/kFBxXNWp7+/P/Xq1bvjI4k2m40LFy7cdPXwxx/HOXlyG0lJiSQnJ2K1ZuPnd+PVQ1X+GVaqRs54uqeWn9aj0J/1ibuZGtWTDUm/MjpuDWb7ICz2zeT9e7qT8+h046lQIZ716zfSqlUrVwcthMtI8vcgg81Efmf+wcEl8yxRo9FQpUoVqlSpQsuWLW+7T3p6eu6HQ2JiIr/9tp+UlHhOn07kwoVE0tIu4Osbdv3qIRKTqdptrh4CcdXVQ5a9O8tPj2fHpZPsvZqOwfY10NyJnhRUquX4+U1l/PgxzJ69Dj+/0n4DXZR0kvw9yJRP8lepMihfvmQmf0cEBATQoEEDGjRoAEC7djffmLZarZw/f/6mD4jjx49w8uSW61cPCSgK+PnlfBhYLJGYzX9fOfz9qozjf9b3csaYyFnTCKzKFJy7Z3ESvf4pqlUzsH79Dho1auREH0J4niR/DzLbjOSV/L29M/D3v/3TJ2WBl5cXkZGRREZG3nGftLS0mz4cTp1K5Pjxr3KvHq5dS0arjcDLKxKj8QrZ2Tu581r6lQA7VsWZKwkrGs1/8fVdxKxZ03juuWdkspYoUST5e4hdsZNlNwF3XrnSyytTVnLMR1BQEEFBQXc8w87OzubcuXPMnj2HlStXAGfJu5CKM4n/AHr9SBo1qsCaNXupUaOGE30IUbRcnvwXLVpEXFwcVquV0aNHExsby4EDB9Drc5LeyJEjad++vasPW+wZrFl4qfywKnc+O9RoMuTJkELSaDQsXvwBn3zyA3AUcOWaOSa8vWfj6/sRb7+9iOHDH5fJWqLEcmny37NnD3/++ScbNmwgNTWVXr168cADDzBv3rxiX1ja3TKtZrzVeqy2O++jVkvyLwyDwUDfvsP48cdLGI2xgCuH0H5Ap3uKDh2asHz5ISIiIlzYtxCe59Lkf9999+VejgcGBmIymUhPT3flIUqsDKsJjSq/IR1J/s46d+4cnTo9SkJCA8zmdYCvi3q+ho/Pi+j137BixRJ69uzpon6FKFouTf4ajQadLmc99Y0bN9K2bVuuXr3Ku+++S3p6OuHh4UyfPp2goCBXHrZEyLCaUecx3g+gKDLm74z9+/fTpUtP0tPHYbVOxnUTyb5Aqx1H166tWbXqKIGBgS7qV4ii55Ybvtu3b2fTpk189NFH7Nmzh1q1alG9enWWLl3K4sWLeeWVV25pEx8f7/TxkpKSsNvt+e9YhDKyTahUeZ/VW63XSE5OLtR7AWA2mwvdhye4Is7t27czadJszOb3gb6uCYxk/PzGERCwn9dem0/Dhg05f/4858+fd1H/7lESfu92u1LUIRQr8fHxRfaUmMuT/08//cT777/P8uXL8ff3p0uXLrnf69KlC7Nmzbptu8LcEzhx4gRqdfEueJJpNYOSd/K32w00bdqU8HDn1pv/278XdiuuChOnoijMm7eI+fMXYzZvxblKWrf0ikq1Cj+/SYwdO5JXX41Bq9WWiffTU9RquUF+o6ioqEIl/7i4OKfbujT5Z2RksGjRIlauXJk7tDNmzBhmzJhBpUqViI2NpXbt2q48ZImRYTVhz3N2L1itMubvCIvFwrBho/nyy4OYTHvIWVSusE6h14+mcuUrfPzxVpo2beqCPoUovlya/Lds2UJqairPPvts7rY+ffowYcIEdDodWq2WBQsWuPKQJUaG1YwtzzN/KzabBa22rFTlcs7ly5d58ME+HDsWjMn0E3nNm3CMDbX6bXx95zN16iQmTXoeLy+Z/iJKP5f+lffv35/+/fvfsv2xxx5z5WFKpIxsE9n28nnskYmvbzl5bjwPx48fp2PHh7lypS8Wy3wKX9vYjl7fnnr1vFi7dneZvSoVZZOc4nhIptVMtpJ3CUetVoZ87mT79u306jUIg2EhijLcRb3aMJl2s2ePpdjfMxLC1eQv3kOuOlC/V5L/7S1Z8j6PPjqEzMyNBUz8SUBGPvuoJPGLMkn+6j3kqhP1e8s6m83G2LHPMmnSW5hMPwPtCtB6F77qhmg1t1bqEkJI8veYNAeqeBW0fm9plp6eTkyk5DYAACAASURBVOfOj7J69RGMxt1ALYfbqlhOOa/e9K3SEBXyXLkQtyPJ30PSs/Mv3u6O+r0l0ZkzZ2jSpBW7d1fFaPyGnPKPjrDho3qBCL9Z/NZpBu1D67szTCFKNEn+HuJI8faiqN9b3OzevZumTVuSmPgkWVlLcbysYyZazWM0CvqOw13nUDegsjvDFKLEk+TvISW5fq+nrFu3ns6de5KWtgybbSKOr9FzFr3mAR6rZOKXjlOo4CsfokLkRx719BCDNf/6vaW5hGNeFEVh+vTZvPXWSozGHUDDArTeh1bzCFOjOjOl7iMyT0IIB0ny9xBH6veW1OLthWEymRg4cATbt5+5vgZ/QdY12ohOM5q1zUfyWOX73RWiEKWSJH8PMTlUv7ea5wIqBlJSUujXbzh//VUdk2kn4OjSFgpeqnkEei/mu7Yv07R8dXeGKUSpJMnfAxRFwSL1e29y6NAhevUaTEbGk2Rnz8Dx8f0s/NQjuEv/GzvazaGSNtidYQpRakny9wCDLQuNygercue3uyzV7/3666/p1+8JjMZ3gIEFaJmCTvMI7UI1bHpgBjovV1XrEqLskad9PODv+r15KQv1exVF4bXX3iQ6+imMxi8pWOI/hk5zH0/XrMxXrZ+RxC9EIcmZvwdkZEv93uzsbJ58cjybNu3GZNoNFOT+xrdoNYNZcs9AnrirIEs8CCHuRJK/B2RYTWW6fm9qairdu0dz6JAfRuMv5P3I683UvEs5r5l81XoibUKLd5UqIUoSSf4ekGE1o8on4dntpfPM/+TJk3To0INLl3pgsbwGOFqyzoqv+hki/Lawo90sapaLcGeYQpQ5Hkv+8+fP5+DBg6hUKqZOnUqjRo08degil5nv0g5gs5W+5P/DDz/w6KP9ycycjd0+ugAtr6HT9KFp0FW+aj2LIJ/CVusSQvybR2747t27l4SEBDZs2MCrr77K3LlzPXHYYiMjO//6vdnZpSv5f/jhCh56qB/p6WsKmPhPo9M0Z0BVb3a1nySJXwg38ciZ/+7du+ncuTMAtWrVIj09nczM0jvG/W8ZVlM+9Xtt2GxZ6HQ6j8XkLna7neefn8KyZZ9iMv0A1C1A61/Qanoxr8EjPFvnQXeFKITAQ8n/8uXL1K//z/K6FSpUICUlpQwlfzNWe2Aee2Ti46Mv8evSGAwGevcews8/X72+VEMFh9uqiEGnmcjGB8bwUMWm7gtSCAF4KPkrinLL1/9OdPHx8U73n5SUhN1ud7q9u+XU762axx4Z+PjoC/Ue3MhsNrusL0ddvHiRESMmcOFCM7KyNgA+Dra04616hfI+K9jRbhoNAiPdGeZt5fdeFcX76YySEKfdLsV1bhQfH49G4+hDEK7lkeQfHh7O5cuXc7++dOkSISEhN+0TFeX8Y3wnTpwo1nVYr2aZUfKp3+vvH1io9+BG8fHxLuvLEfv27aNPn6Gkpz+DzfYSji/VYESrHkId/z/Y1nYOYX55XR25T37vlaffT2eVhDjV6pJ9detqUVFRhUr+cXFxTrf1SMZs1aoVW7duBeDYsWOEhYWVmSEfgNTs/Ov36nQl8/3YuHET7do9RGrqu9hsk3A88V9Ap2nFQxWvsqfT1CJL/EKUVR4587/nnnuoX78+AwYMQKVSMXPmTE8ctthIs+RfwrGk1e9VFIW5cxewcOH7GI3bgIKM0/+OVtODF+9uy6x6vUr8vQ4hSiKPPef/4osveupQxc41B0o4lqT6vVlZWQwZ8hTffHMMo3EPUKkArb9ApxnOivsep1/Vlu4KUQiRD5nh6wHp2aWnfm9KSgrduvXm+PFwTKYfAUcfT1XQqF4jwOt1vm37EvcH13JnmEKIfEjy94CcGb55j/kHBhb/Mf9jx47RqdMjXLkygOzsuTh+y8iCn3o0VXQ/saPdbCJ1Ifk3EUK4lSR/DzBY867iBcW/hOPWrVvp23coBsPrKMqwArS8ik7TkwcqWPi81UzKefm5LUYhhOOK7/ORpYjJlv+wT3FO/osXv0evXo+TmflpARP/CXSa+xhRPZitbZ+XxC9EMSJn/h7gWP3evCaBFQ2r1cq4cc+zZs12TKZfgJoFaL0TraYfbzbpy6gandwVohDCSZL83UxRFLLsRvIa8/f2Ln7rHF27do1HHhlAXJwNo/FXIMjhtir+RzmvKXzRajwdwhq4L0ghhNMk+buZ0ZaFRuVdour3nj59mo4dH+HChXZkZb2N438mNnzULxLqu4md7WZQx78gj4AKITxJkr+bZVrNeKn0WPNY0qQ41e/99ddf6d69DxkZU7HbJxSgZSY6TT8aBJ7nmzZzCPYpXlcyQoibyQ1fN8uwmvFSl4z6vTExa+nc+TGuXfuogIk/Eb2mBb0qZ/NTh8mS+IUoAeTM380ysot//V673c6UKTN59901mEw7gYKM0+9Fq3mUV+p1Y9LdPWSpBiFKCEn+bpZhNaFSFd/6vUajkf79n+D7789dX4M/rACtN6DTjGV9i6d4tFIzd4UohHADSf5uVpzr9164cIHOnXty6lQdzOYdgKPP4St4qeYQ6L2U7e2m0CToLjdGKYRwB0n+bpZhNWPPs4Rj0dTv/f333+nSpSdpaU9htU7D8aWYzfiph1Oj3AG2t51DRW15d4YphHATSf5ulpHtSP1es0fr927evJmBA0diNC4B+hWg5SV0mofpGObDhhbT0Xn5uitEIYSbydM+bpZhNWFV8qriZcDHR+eRSmSKorBw4RsMGDAWo/FrCpb4j6DTNGN8rWp80WpCiUj8OTefbXnsocHHpwpPPDGGa9eueSosIYoFSf5ulmk1k51n8fYM/PzcP+RjsVgYNmwUc+fGYDLtBu4vQOst6DTtWHpPTxY26odaVTL+bAK9dWhUqXnsocZsPsCGDXZq1GjA5s2bPRabEEXNZcM+VquVadOmkZSUhNVqZdKkSTRr1owxY3LOqry8cg41efJkGjQoO1P+Uy1Z+dbv1encm/yvXr3KQw/15ciRchiNP5P38tI3UlCzGH/vOXzd+llahdR1Z5guV1MfDnyVz15BmM3/w2zexcCBT9Gx41qWL3+H8PBwT4QoRJFxWfL/4osv0Gq1rFu3jj///JMpU6awadMmDAYDH3zwAQEBeSXA0uuqJf/6vXq9+5L/iRMn6NjxYVJSHsViWQg4Wizaiq96PBF+3/J9+9lU1xfkEdDioUFgVbLt54FkIL9k3h6j8RDbts2idu1GvPPOIh5/fJjMWxCllsuu3x999FGmTJkCQHBwMGlpaQAYDAZXHaJESnOgipde754JXt9//z3NmrXh/PlJWCyv43jiT0On6Ubz4H0c7FoyEz+At9qLhyKaoWKdgy20WCwLycj4hvHj36J1626cPn3arTEKUVRcdubv7e2d++9Vq1bx8MMPAzmTiGbPns2FCxeoU6cOU6ZMwdf31puF8fHxTh87KSkJu93udHt3upadf/F2Ly9NoX7+fzObzcyePZf//GcxZvMGoEMBWp9Cp3mQIZF1WHLPU3ipHf3AKJ4m1+3C1uTXMdpG43jJyXswGPYSG/sG9eo1Y8yYJxg5cjgaTfF+L8xms0v/jtzBbs9jkasyKD4+vsj+rpxK/hs3bmTjxo03bZswYQJt2rRh7dq1HD16lPfffx+A0aNH06pVK0JDQ5kxYwZr165lxIgRt/QZFRXlTChAztCGJ56WcYYj9XsrVgwv1M9/I5vNxuOPP8Vnn/2M2fwzUKcArX9Cq+nNgoY9eaZ2N5fEU9SaV6hNp7CabE1+GYv9nQK09MZmexmbrQ8ffDCS7777mfXrl9OwYUO3xVpY8fHxLvs7che1WobRbhQVFVWo5B8XF+d0W6eSf3R0NNHR0bds37hxIzt37uS9997LvRLo1atX7vc7d+7Mli1bnAy1ZMq0mshvzD8oyDVj/pmZmfTqNZiff76G2bwHCHa4rYpV6L2eY9MDY+kW0cQl8RQXK+57ggbbXuGSuQ52xhewdW1Mpl0cO7ac5s07MnHiWGbNmnbbq1chShKXnS4nJSXx8ccf8+677+b+x8g5C32czMxMAGJjY6ldu7arDlkiGKwm8jvzDwoq/Jh/UlISTZu25uefQzGbt+F44rfjrZpMmO8UYju9UuoSP0AFX39+6TCFcL//4KseCxT0PpQaRRmFyfQ777xziDp1mvLrr7+6I1QhPMZlyX/jxo2kpaUxatQohg4dytChQ7HZbPTu3Zthw4YxePBgLl68yODBg111yBLBaMs/+Re2fu/evXtp3LgFp08PxWxeBvg42NKAVtOL+oFfc7jbXOoFVClUHMVZjXLhHOv2Kg9XPI5OEwV850QvlTEaPyMxcQ6dO/dl1KgJZGRkuDpUITzCZTd8n3/+eZ5//vlbtvfs2ZOePXu66jAljiP1ewMCKjvd/4YNnzBixDiMxg+BRwvQ8jx6TXceqlieNfdPxVfjnX+TEi7IR8+mlk/zzYUDDNs7lExrF8z2tynI8FjOGkh9MZk6EhPzIp991oBVq5bSvXt3N0UthHsUz7ukpYQj9Xu9vDKdWtRNURRmznyV4cNfxGj8joIl/v1oNc2YdHc9Pmkxtkwk/hs9VLEpp7ovYli1VLSausAGoKBPoQRjNn/E5csfEh09nt69B5OSkuKGaIVwD0n+bmSyWVCrvIA7J1cvr4wCF3Ixm8307TuUN97YjMkUCxRknP4zdJrOrL5/IDPq9yqzk5j8vbV80OxxdrSbSKRuMjrNw8A5J3rqjNF4mK+/jqBWrYasWbMWRZHHGUXxJ8nfjTKtZrxVeVfxKmj93kuXLtGiRSe++caCwbALqOhgSwWNagHlvUfzQ/tJ9K3SwuFjlmYPVKjDiQfn82ztcmg1DVGxFCjonBE9FssbpKdvZsyYhbRv34OEhAR3hCuEy0jyd6MMq8ml9XuPHDlCw4bNOXasIybTxzg+acmCn/oJaug/5FDXOTQLrulgu7LBV+PNvIZ92dtpGvUD3kGvaQOccKKn+zEY9vHrry2pV+9e3nprcbGdfCiEJH83yrCa863fC46N+X/77be0aNGRlJS5ZGfPxfFf3WV0mg60CT3B/i4zqaKr4GC7sqdBYCS/d53FnPp10Gmao1HNB7IL2IsPVut0jMafmD59A02btubYsWPuCFeIQpHk70YZ2Y7V781vzP+ttxbTu/dwDIbPUJQhBYjgODrNfYyqEca3bZ6lnJejZRrLLo1KzfN3d+dot1dpEfwpes09gDOzKKMwGH7k8OEhNGvWlldemYPFYnF1uEI4TZK/GzlSv9dqvfOwj9VqZeTIcUyb9j4m069AqwIc/Tu0mla83eRB3mwyqMSswV9c3KUP46cOk3nvnnb4e3XFW/UCYCxgL2oU5WlMpgP89797qVv3XmJjY90RrhAFJhnBjTKspnzr994p+aelpdGhQw8+/vgURuOvQHWHj6tmKf5eA9jSegJP1uhY0LDFdSqVimF3tePkQwt5MOI3dJr6wPdO9FQVo/FLTp+eSocOPXn66efK/Gq3ouhJ8nejDKs5n/q9dqxWE3r9zfcFTp06RePGLfntt7sxGr8E8qoEdiMbPupnqKRdQFznmbQPq+9s6OIGYX6BbG49gY9b9KOCz0D81COAtAL2ogIGYjIdYeXKy9So0YBt27a5IVohHCPJ341yirfnXb/X21t704qkP//8M02btuLs2fFkZb2D45OwM9BpetA06EcOdZ1NbX9HHwEVjnqkUjNOdV/IwMgL15eI+D8negnBZIrh0qWl9Oo1iv79n+DKlSuuDlWIfEnyd6NMqxlLAer3rly5mq5de5OevhK7/ekCHCkBnaY5faso/NRhMuV93FMcRkCAt46P7hvBt23GUln7LDrNY8BFJ3p6EKPxMF98EUjNmg3YsGGDTA4THiXJ341Ss80O1e+12+289NI0xo2bjcm0CyjIWvp70GruZ1b9+1l530i81S5brknkoU1oFCcfWsDTNTVoNfVRsZyCLxHhT1bW21y79n+MHDmHzp17cvbsWXeEK8QtJPm7kSP1e728NDz8cD/ee+9HjMY9QL0CHGE9ek13PmkxnJfu7lFml2ooKn4aH15rPIDdHV/mbv/X0GvaA3850dMDGAz7+fHHe6hbtynvvfe+TA4TbifJ343Ssy3knfwzOHv2ON9/r8do3A6EOtizgrdqJqG+z/Nrx6k8XOnewgcrnNY46C4Od53N9HrV0GqaoVEtAqwF7MUXq3UWBsP3TJq0kvvv78Aff/zhjnCFACT5F7EHgG8xm1cCjlaGMqFVD+Bu/0841HUOjYKquS884TAvtYaX6z7C4a5zaFZ+PXpNM+CgEz01wGD4hQMHetO0aSvmzJlPdnZBZxkLkT+XJf+tW7fSpUuX3EIuS5cuBeD48eMMGDCAAQMGMHPmTFcdrkSopNUDyXns4UvO+L6jwzXJ6DVt6RJxgb2dpxPhF1ToGIVr1SwXwe6OU3iryQOU8+qAt2oKYC5gLxrs9omYTPtYuPAH6tW7j3379rkjXFGGuSz5G41GBg8eTExMDDExMYwdOxaAefPmMXXqVD7++GPS0tL44YcfXHXIYq9xYCX0mgMu6u0wOk0zJtauwectx6PVOFqtS3iaSqXiyRodOfHgf+gc/iN6TQPgJyd6uguj8VtOnnyBtm17MHHiSxiNBZ1lLMTtuSz5327GosVi4dy5czRq1AiATp06sXv3blcdstjrEFYfOzsAWyF7+gqtph3LmvVmXsO+cmO3hKioLc+WNs8S07wX5b374KseBaQXsBcVMBST6TDLlp2lVq1G7Ny50w3RirLGpWf+3333HSNGjGD48OEcP36c1NRUAgL+edQxNDS0TFU7qlkugrt0IcBXTvagoFH9lyDv4exo9wKDIlu7MjzhIb0q38+p7ouIrnIGnaYusNmJXsIwmdZz4cJbPPzw4wwe/CSpqamuDlWUIU49FL5x40Y2btx407bOnTszYcIEWrRowb59+3jppZdYvnz5TfvkNYklPj7emVAASEpKKraPxr3aoAfD9k7FYOtOXhW9bpWNr/ppKml3sLPdLO7Sh7krROEBQT56Ypo/xYhLRxgc+zRp2TGYbEuAgv5eH8ZkasumTZP46qt6zJnzMl27dgVyKrwV5v+RJ9jtMpHtRvHx8Wg0miI5tlPJPzo6mujo6Dt+v1mzZly9epXy5cuTlvbPGijJycmEhd3+jz0qKsqZUAA4ceLETUskFCe9Kt9P0/K7iL0yjWxlkYOtUtFpenFfsIHNrWYS4O1o0RZR3HUIa8Bf3Rcy9fAmPjhVD5PtDWAYjt/0BwjAYnkfi2UwU6c+yTff/MCKFUtIS0sr1P8jT1CrZcjyRlFRUYVK/nFxziw3nsNlGXPJkiVs3boVyEnGwcHB+Pj4UKNGjdwnFbZt20abNm1cdcgSQaVS8X8txxLiu+56cZD8znz+RKe5n2HV/Nne9gVJ/KWQVuPDm00G8XOHl6hd7lV0mi7AGSd6aoPReJCdO6OoXbsRn3yySZaIEA5zWfLv2bMna9asYciQIcyYMYN58+YBMHXqVP773/8yYMAAIiMjadmypasOWWKE+gawt9N0aupXoNN0B25X2cmEirfQaVrwWqOOLL13GF7qorkcFJ5xT/kaHO02hyl1I9BqmqLmLQr+cIAf2dnzMBi2s3DhZ7Ro0YmTJ0+6I1xRyrhsIZgqVaoQExNzy/ZatWqxbt06Vx2mxKqiq8ChrrN548QWFh5vA1TCptyDTdHioz5Dln03LStEsbjpNOoHVi3qcIWHeKu9mF6vJ/2q3segPR9yPGMNBtsqoKDLcTfGZNpLXNzbNGrUgldemcxLLz2Hl5es9SRuT/4yPMhX483UqJ68dHcP9l49SXz6Ocz2bCr5NaBlSB+ZtFWG1fGvxN7O0/jg1A5eOtiaLPt4rMp0HJ/5DeCFzfYCJtNjvPrqKFav3sD69ctp0qSJu8IWJVjxvEtaynmrvWgVUpcna3RifK0H6V2luSR+gVqlZmzNLvzx0H9oH/odek0jwJl5MTUxGrfzxx9P07JlV158cSpmc0FnGYvSTpK/EMVMZW0w29o+z4r7ehDo/Si+6nFAZgF7UaEoIzCZDvLeeyeoVasxP/74ozvCFSWUJH8hiiGVSkV01Qc41X0Rj1U+fr1y2DdO9FQRk2kT5879hwcfHMgTT4zh2rVrrg5XlECS/IUoxoJ9yvFxizF83uoJwn1HolUPAi470VMvTKajbNhgp0aNBmze7MwsY1GaSPIXogToEt6Iv7ovZHj1TLSaKGAdBa8cFoTZ/D+uXl3NwIEv8Mgj/UlOzmvVWVGaSfIXooTQe/mx5J6h7Gr/PNX109FpHgKSnOipA0bjIbZtu4vatRuxcuUqmRxWBknyF6KEuT+4FscfnMdLd5dHq2mMmneBgq5tpcViWUhGxjeMH/8WrVt34/Tp0+4IVxRTkvyFKIF81F7Mqt+buM6v0CjwffSalsBxJ3q6B4NhL7GxHWnQ4D5ef/1NbLbCLkEuSgJJ/kKUYFEBVYjr8grzGzZAr2mJl2oOYClgL97YbC9jNP7KrFmf07hxSw4fPuyOcEUxIslfiBJOrVLzTO1uHHtwHq1CvkKvaQL85kRPdTAYvufYsZE0b96RKVNmkJWV5epwRTEhyV+IUiJSF8L37V7kf826EOD1ID7qZ4FbK+zlTY2ijMJk+p133jlEnTpN+fXXX90RrihikvyFKEVUKhWDIlvzV/dFPFzxd3SaesB2J3qqjNH4GYmJs+ncuS+jRk0gIyPD1eGKIiTJX4hSKMQ3gE9bjmPTA4MJ8RmCn/px4GoBe1EB0ZhMR4iJyaRGjQZs2bLFDdGKoiDJX4hS7KGKTTnVfRHDql25PjnsEwo+OSwYs3kFly8vJzp6PL17Dy5TtbhLK0n+QpRy/t5aPmj2ONvbTiBSNwmd5hHgnBM9dcFoPMzXX0dQq1ZD1qxZK5PDSjCXree/dOnS3BtDdrudy5cvs3XrVsaMyVlI6u+iEpMnT6ZBgwauOqwQwkEtQ+7mxIPzmX3sc976syFm23wURlGwc0A9FssbWCz9GTPmSZYtW0tMzPtERka6K2zhJi5L/mPHjmXs2LEAfPbZZ1y5cgUAg8HABx98QEBAgKsOJYRwkq/Gm/kNoxkU2ZyBe97mtGENBtsKoHYBe7ofg2Efv/66iKioe5g/fxYTJjyNWi2DCSWFy39TVquV9evXM2TIECAn+QshipcGgZH83nUWs+vXRqe5H41qAZBdwF58sFqnYzT+xLRpH9O0aWuOHbtdfWpRHLk8+W/bto3WrVvj5+cHgNFoZPbs2QwaNIhZs2bJpBEhigmNSs0Ld3fnaLdXaRG8Cb3mXmC/Ez1FYTD8yJEjg2nWrC2vvDIHi6Wgs4yFpzk17LNx40Y2btx407YJEybQpk0bPv30U2bPnp27ffTo0bRq1YrQ0FBmzJjB2rVrGTFixC19xsfHOxMKAElJSdjtBV3YSggBcJc+jJ86TCYm4UfGH+hClm04FmUuoC1AL2rs9nGYTI/w+uujWbmyEa+9NovGjRvftJfdLjeIbxQfH49GoymSYzuV/KOjo4mOjr5lu9FoJDk5mSpVquRu69WrV+6/O3fufMfnhKOiopwJBYATJ07IWKMQhaBSqRh2Vzu6RTTmqX0x7LhUD6NtBdC+gD1FYjZv4ezZ9YwY8SxPPDGQ1157Fb1eD4BarXJ16CVaVFRUoZJ/XFyc021dmjGPHz9O9erVc7+22Ww8/vjjZGbm1B+NjY2ldu2C3lgSQnhKuF8Qm1tP4OMW/Qj26Y+feiSQVsBeVMAgTKYjrFx5mRo1GrBt2zY3RCsKw2VP+wCkpKQQHByc+7VGo6F3794MGzYMrVZLeHg4EyZMcOUhhRBu8EilZpzqXo/nfv+YDUlRGG3vAb3ybXezEEymGEymb+jV6ykefrgDNpvVHeEKJ6iUYjBLIy4ujnvvvdfp9l988QXDhn1EevoXd9zHT12ZAG8VapUMDwlREFeykslWLMBuoIWTvWTg6zsNRdmExfIXd7qf4KN+HYv9JSL8qjp5nOLBZDNgsUVjsr9/x31UKg3Z2ZZCD/s4mztdeuZfnJntBzFnFXRtEyHEP2oUoq0/WVnvAG8Cd052FvtzwKNcNBfiUMVG8f4AKzPJH0Kuv4QQRSe/s1wNUMcTgZR5MgYihBBlkCR/IYQogyT5CyFEGSTJXwghyiBJ/kIIUQZJ8hdCiDJIkr8QQpRBpeI5/4iICDIzt6DR+BV1KEII4ZDAwHBUqqJb6K5UJP/mzZtjNGa6vZ7o8ePHqVu3rluP4QoSp2tJnK5VEuL0RIwajaZIVyMuFckfwNfX1yPH+LtITXEmcbqWxOlaJSHOkhBjYcmYvxBClEGS/IUQogyS5C+EEGWQJH8hhCiDnE7+e/fu5YEHHuD777/P3Xb8+HEGDBjAgAEDmDlzZu725cuX07dvX6Kjo/nhhx8KF7EQQohCc+ppn8TERFasWHFLBZl58+YxdepUGjVqxMSJE/nhhx+oUaMGW7Zs4eOPPyYzM5MBAwbQunXrIqtYL4QQwskz/9DQUN59913KlSuXu81isXDu3DkaNWoEQKdOndi9ezexsbG0adMGHx8fgoODqVy5MidPnnRN9EIIIZzi1Jm/Vntr/c3U1FQCAgJyvw4NDSUlJYWgoKCbirqHhISQkpLC3XfffVP7+Ph4Z0LxKLPZLHG6kMTpWhKn65SEGAsr3+S/ceNGNm7ceNO2CRMm0KZNmzzb/T3b9t+zbhVFue2U5qioqHyDLWrx8fESpwtJnK4lcbpOSYgRcgq4Oyvf5B8dHU10dHS+HQUHB5OWlpb7dXJyMmFhYYSHh3P69OmbtoeGhjoZrhBCCFdw2aOe3t7e1KhRg3379gGwbds22rRpQ4sWLdi1axcWi4Xk5GQuXbpErVq1XHVYIYQQTnBqzH/Xrl18+OGHnDp1eY09PgAABv1JREFUiqNHjxITE8NHH33E1KlTmTFjBna7ncaNG9OyZUsA+vXrx5AhQ1CpVMyaNatIFzMSQgjhZPJv37497du3v2V7rVq1WLdu3S3bhw4dytChQ505lBBCCDeQU3AhhCiDJPkLIUQZJMlfCCHKIEn+QghRBqkUd9c+dEBhJioIIURZ9u811hxVLJK/EEIIz5JhHyGEKIMk+QshRBnk8eRvtVqZPHkygwYNol+/frnLQRS3QjC3K1YzZswYBg4cmDtp7ciRI0Ua453iLG7v5Y22bt1Kly5dct/DpUuX5hlzUZo/fz79+/dnwIABHDp0qKjDyXXkyBHatm2b+x7OnTuXCxcuMHToUAYNGsTEiROxWCxFGuOJEyfo3Lkza9asAbhjfJs3b6ZPnz5ER0ezadOmIo9z7ty59O7dO/e93bVrV5HHuWjRIvr370+fPn3Ytm2b695LxcM2bdqkzJw5U1EURTlx4oTSp08fRVEUZciQIcrBgwcVRVGUZ555Rtm1a5eSmJio9OrVS8nKylKuXLmidOnSRbFarW6PMSEhQRkzZowybtw4ZefOnbnbhwwZoly7du2mfYsqxvziLC7v5b/93//9n7JixYpbtt8u5qIUGxurjBo1SlEURfnzzz+Vvn37Fmk8N4qNjVVeffXVm7a9/PLLypYtWxRFUZSFCxcqa9euLYrQFEVRFIPBoAwZMkSZPn26EhMTc8f4DAaD0rVrVyU9PV0xmUxKt27dlNTU1CKP89ixY7fsV1Rx7t69W3nyyScVRVGUq1evKu3atXPZe+nxM/9HH32UKVOmAP+sBFrcCsHcrlgNgMFguGXfoixWUxKL6tzuPbxTzEVp9+7ddO7cGchZtiQ9PZ3MzMwijelvd/o77NSpE1D075+Pjw/Lli0jLCwsd9vt4jt48CANGzbE398fPz8/mjVrxv79+4s0ztu9t0UZ53333cfbb78NQGBgICaT6f/bO5eQVPo4DL9y1FII8taAO7HCCLKF0EVok9UmgloVBBEEBSW0KMyQLouwQtpoZaCChVDkJqIoiKDLJrA2XVZB0E1IEzLUCsOziM+jZuecvi7jwf+zmYuzeHhxfsiMM++nZfm/3u3zEVgsVnTdbrejtrb2w0Uwn02yshoACAaDGB4ehtvtRn5+PrRaLbxeLy2Ob3mmWpaJBINBbG1tYXt7G5FIBBqNBjweL6kznXi9XhQWFka3BQIBPB7Pqx8EdBAMBrG/v4+2tjaEQiGo1WqEQiGw2WwA9OfHZDLBZMaPlmR+b507dHoGAgGYTCb4/X5QFAWdTker548fP8DlcgG8dKtUVFRgd3f3U7L80uH/uyIYh8OB4+NjmM1m+Hy+uGMi7yyC+SrHRNrb26FUKiESiTAwMACHw/Etju/1TPSJXcbu/wrPWJI5q1QqqNVqlJaWwuVyobe3FxaLJakzndCR198ik8nQ2dmJyspKnJ2dobW1FeFwOPp5KuSXSGx2dH4n/0RjYyNyc3MhkUgwPT0No9EIuVwedwwdnhsbG3A6nbDZbKipqYlziV2+x/FLh/9bRTCLi4vY3NzE1NQUWCwWrUUwf1tWAwD19fXRdZVKhdXVVZSUlHxLWc2/WKrzJ2eFQgGfzwcej5fUmU4oioLX641u39zcQCgU0mj0C6lUCqlUCgCQSCQQCoVwu914eHhAZmZmSuSXCIfDeeVHUVT0hirwknFxcTF9kgCqqqri1oeGhlBdXU2r587ODsxmMywWC7Kysj4ty2+/5n9xcYH5+XmYTCZkZGQA+DeKYJ6fn9HS0hK97ru3t4e8vLyUcgRSP8vJyUmsr68DePmnBZ/PB5vNTupMJ0qlMup5cnKCnJyclLjkAwBOpxOzs7MAAI/Hg9vbWzQ0NER9UyG/RMrLy1/5yeVyHB4ewu/3IxAI4ODgAAqFglbPjo4OXF9fA/h1jtPpeX9/j/HxcczMzCA7OxvA52X57U/4TkxMYGVlBWKxOLrParXi/Pw8rgjmv5vCc3NzWF5eBoPBQHd3N8rKyr7cMbashs/nQyQSwWazYWlpCXa7HRwOBxRFYWRkBBwOhxbH33menp6mTJaJXF5eQqvVIhKJIBwOo7+/H0VFRW8604nBYIDL5QKDwcDg4CBkMhndSgCAu7s79PT0IBgM4unpCV1dXSgoKIBGo8Hj4yPEYjH0en3c/bXv5OjoCGNjY7i6ugKTyQRFUTAYDOjr63vlt7a2BqvVCgaDgebmZtTV1dHq2dTUBKvVCi6XCw6HA71eD4FAQJvnwsICjEYjJBJJdN/o6Ch0Ot2HsySvdyAQCIQ0hDzhSyAQCGkIGf4EAoGQhpDhTyAQCGkIGf4EAoGQhpDhTyAQCGkIGf4EAoGQhpDhTyAQCGkIGf4EAoGQhvwEODMa7g0eJXAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a negative distance on a buffer can be used to erode a polygon\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "patch1 = PolygonPatch(poly_with_holes,fc='#0000FF',alpha=1)\n",
    "poly_eroded = poly_with_holes.buffer(-10)\n",
    "patch2 = PolygonPatch(poly_eroded,fc='#FF55AA',alpha=1)\n",
    "p1 = ax1.add_patch(patch1)\n",
    "p2 = ax1.add_patch(patch2)\n",
    "ax1.set(xlim=[-200,200], ylim=[-110,110])\n",
    "ax1.legend({'original polygon':p1, 'eroded':p2},loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 208
    },
    "colab_type": "code",
    "id": "EhRdZKYEqF35",
    "outputId": "c09c76ac-95a3-40cc-fcd1-15e4e986dbf9"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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      ],
      "text/plain": [
       "<shapely.geometry.multilinestring.MultiLineString at 0x7feeff98fc90>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the outline of an object with .boundary\n",
    "poly_eroded.boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "-t1DgfRUgTQ2",
    "outputId": "3b343aae-6278-4e88-86f4-3a67be0d2e32"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1714.7439056131875"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# length of the boundary\n",
    "poly_eroded.boundary.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "OEraGbQDe0y8",
    "outputId": "b207971c-ac84-4790-8dd8-44a28156753e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31298.780262343378"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the area of the shape\n",
    "poly_eroded.area"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Minimum bounding upright rectangle\n",
    "\n",
    "Often, it's useful to know the smallest possible upright rectangle (i.e. with sides parallel to the axes) that can be drawn around a polygon. So, in this exercise, you will do just that: given a polygon, plot its minimum bounding upright rectangle and return it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getBoundingRectangle(poly):\n",
    "  \"\"\"\n",
    "  input: poly, Polygon - any valid shapely Polygon object\n",
    "  output: rect, Polygon - the minimum bounding upright rectangle\n",
    "  Also plot the input Polygon as well as the bounding rectangle itself\n",
    "  \"\"\"\n",
    "  # fill this in with your code\n",
    "  return rect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Tip: The `bounds` attribute of the polygon would be useful here.<br>\n",
    "Also, the Shapely `envelope` attribute, which will be mentioned later, calculates this; try to do it without using `envelope`._\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hGKofT8HiYdj"
   },
   "source": [
    "## Geometry Collections\n",
    "Geometry collections are datatypes that store multiple geometry objects. Much like how lists store multiple individual objects in a larger data structure, geometry collections do the same with shapely objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UBuR32YZiuQK"
   },
   "outputs": [],
   "source": [
    "# Import collections of geometric objects + bounding box\n",
    "from shapely.geometry import MultiPoint, MultiLineString, MultiPolygon, box\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "xQ0jXNe3iw8u",
    "outputId": "13309c84-5e5c-4d29-99e8-7b291c8f34e2"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"1.028 -26.272000000000002 9.404 31.644000000000002\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-20.900000000000002)\"><g><circle cx=\"2.2\" cy=\"4.2\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"7.2\" cy=\"-25.1\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"9.26\" cy=\"-2.456\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /></g></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.multipoint.MultiPoint at 0x7feeff80cbd0>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a MultiPoint object of our points 1,2 and 3\n",
    "multi_point = MultiPoint([point1, point2, point3])\n",
    "multi_point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "4Z47GliyiznK",
    "outputId": "6741a825-ee59-4c6e-fd9b-5a1edc55c9ef"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"1.028 -26.272000000000002 9.404 31.644000000000002\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-20.900000000000002)\"><g><circle cx=\"2.2\" cy=\"4.2\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"7.2\" cy=\"-25.1\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"9.26\" cy=\"-2.456\" r=\"0.9493199999999999\" stroke=\"#555555\" stroke-width=\"0.31644\" fill=\"#66cc99\" opacity=\"0.6\" /></g></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.multipoint.MultiPoint at 0x7feeff85bd90>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# It is also possible to pass coordinate tuples inside\n",
    "multi_point2 = MultiPoint([(2.2, 4.2), (7.2, -25.1), (9.26, -2.456)])\n",
    "multi_point2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "kKDijf4Ci7y_",
    "outputId": "e57d07ea-4ed9-4a66-ad06-4546c9963931"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"1.028 -26.272000000000002 9.404 31.644000000000002\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-20.900000000000002)\"><g><polyline fill=\"none\" stroke=\"#66cc99\" stroke-width=\"0.63288\" points=\"2.2,4.2 7.2,-25.1\" opacity=\"0.8\" /><polyline fill=\"none\" stroke=\"#66cc99\" stroke-width=\"0.63288\" points=\"7.2,-25.1 9.26,-2.456\" opacity=\"0.8\" /></g></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.multilinestring.MultiLineString at 0x7feeff861650>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can also create a MultiLineString with two lines\n",
    "line1 = LineString([point1, point2])\n",
    "line2 = LineString([point2, point3])\n",
    "multi_line = MultiLineString([line1, line2])\n",
    "multi_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "GUPxhXSSjAGC",
    "outputId": "e5db35bf-2795-4b8f-cac2-f984445a32fd"
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<shapely.geometry.multipolygon.MultiPolygon at 0x7feeff868290>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# MultiPolygon can be done in a similar manner\n",
    "circle1 = Point(0,0).buffer(1)\n",
    "circle2 = Point(2,5).buffer(5)\n",
    "circle3 = Point(10,10).buffer(7)\n",
    "circle4 = Point(10,11).buffer(3)\n",
    "multi_circle = MultiPolygon([circle1, circle2, circle3, circle4])\n",
    "multi_circle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
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    "colab_type": "code",
    "id": "wZJXyXMjjFab",
    "outputId": "f47ce997-68b8-4e3b-ee1a-59b6ef2d0129"
   },
   "outputs": [
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      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff9a7690>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multi_circle.buffer(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OEpI5p6vkpEj"
   },
   "source": [
    "## Geometric analysis\n",
    "Shapely includes a ton of useful functions to analyze [geometric relationships between shapes](https://shapely.readthedocs.io/en/latest/manual.html#predicates-and-relationships).\n",
    "\n",
    "For example, you can find whether one shape [contains](https://shapely.readthedocs.io/en/latest/manual.html#object.contains) the other within its interior; whether one object [crosses](https://shapely.readthedocs.io/en/latest/manual.html#object.crosses) or [overlaps](https://shapely.readthedocs.io/en/latest/manual.html#object.overlaps) another. _Note that these methods have very precise definitions. For example, `overlaps` and `intersects` are two distinct methods with subtle differences. Refer to the documentation to ensure that you're using the function that you actually want._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "8vQ-gWOzjY1h",
    "outputId": "7caf7c72-2369-4821-9312-4364d85579e2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in order for two objects to cross, one must go all the way through the other\n",
    "circle3.crosses(circle4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "Uzl0lzvKmsv0",
    "outputId": "833953ab-bf9a-424d-97ca-6a068a41b4cb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# intersect checks if any part of the interior of one object is in the other\n",
    "circle3.intersects(circle4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "w5LmTvd1auav",
    "outputId": "a60a0f88-e2b0-4d32-fff5-b8d3b7919ac0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# overlap does not allow one object to fully contain the other\n",
    "circle3.overlaps(circle4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Kyzqljxxbnsr"
   },
   "source": [
    "### Set theoretic functions\n",
    "You can use shapely to do set-theoretic operations, such as intersection, union, and difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "XGqRQRYtbU1U",
    "outputId": "b8fc6298-29cc-4a27-d99e-f4d584ba7be5"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff8026d0>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# intersection represents the shape that is part of both objects (logical AND)\n",
    "circle2.intersection(circle3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "4HX8FQ-fbjoV",
    "outputId": "5759c34b-dd80-4d55-c897-33e9aab746ed"
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff8024d0>"
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     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# union is the shape that's part of either object (logical OR)\n",
    "circle2.union(circle3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "IPjEQZcscjMi",
    "outputId": "42652872-61e4-4995-b911-13ad51c40758"
   },
   "outputs": [
    {
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       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"2.44 2.44 15.12 15.12\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,20.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.3024\" opacity=\"0.6\" d=\"M 17.0,10.0 L 16.966293086705377,9.313880017693076 L 16.865496962822615,8.634367745887104 L 16.698582350125463,7.968007259218766 L 16.46715672757901,7.3212159734443745 L 16.173448850438486,6.70022284221802 L 15.820287286117818,6.111008368862787 L 15.411073173539162,5.559247010854485 L 14.949747468305837,5.050252531694172 L 14.440752989145523,4.588926826460845 L 13.888991631137221,4.1797127138821875 L 13.299777157781989,3.826551149561519 L 12.678784026555636,3.5328432724209957 L 12.031992740781245,3.3014176498745407 L 11.365632254112906,3.1345030371773888 L 10.686119982306934,3.0337069132946226 L 10.00000000000001,3.0 L 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      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff893550>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# difference is the part of the shape of one object that's not in the other (logical AND NOT)\n",
    "circle3.difference(circle4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 171
    },
    "colab_type": "code",
    "id": "YOOdLav3c1VB",
    "outputId": "2a84db09-f9b3-44bf-9468-4d306b6c22f7"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" />"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff7e9410>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note that the order of difference matters\n",
    "circle4.difference(circle3) # is empty because circle4 is entirely in circle3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "4MWu-onec6Tw",
    "outputId": "dc666b59-40eb-4fec-9838-8010023fa9e0"
   },
   "outputs": [
    {
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       "<shapely.geometry.multipolygon.MultiPolygon at 0x7feeff832910>"
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     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# symmetric difference is the opposite of intersection (logical XOR)\n",
    "circle3.symmetric_difference(circle2)"
   ]
  },
  {
   "cell_type": "code",
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    "id": "JWeC0CsHdP9g",
    "outputId": "d18feefe-f01c-4800-cb5b-2b11ef029b7d"
   },
   "outputs": [
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       "<shapely.geometry.multipolygon.MultiPolygon at 0x7feeff997250>"
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     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# appropriately, symmetric difference order doesn't matter\n",
    "circle2.symmetric_difference(circle3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9c4-2XT2dvRP"
   },
   "source": [
    "### Constructive methods\n",
    "These methods create new objects not derived from set-theoretic analysis.\n",
    "\n",
    "We've already seen some, such as `.buffer()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fZJoIzM2dpux"
   },
   "outputs": [
    {
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       "<shapely.geometry.polygon.Polygon at 0x7feeffa07710>"
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     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# get the region around a line\n",
    "buffered_line = LineString([(0,0),(5,5),(-1,5)]).buffer(1)\n",
    "buffered_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
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    "id": "9AD9YIp_eHSJ",
    "outputId": "36612170-f135-482f-ed51-459d521ca079"
   },
   "outputs": [
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     "data": {
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       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-2.32 -1.32 8.64 7.640000000000001\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,5.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.1728\" opacity=\"0.6\" d=\"M -6.049014748177263e-16,-1.0 L -0.09801714032956109,-0.9951847266721968 L -0.19509032201612864,-0.9807852804032304 L -0.2902846772544626,-0.9569403357322088 L -0.3826834323650899,-0.9238795325112867 L -0.4713967368259977,-0.881921264348355 L -0.555570233019602,-0.8314696123025455 L -0.6343932841636454,-0.7730104533627371 L -0.7071067811865475,-0.7071067811865476 L -0.7730104533627367,-0.6343932841636458 L -0.8314696123025448,-0.5555702330196028 L -0.8819212643483547,-0.47139673682599825 L -0.9238795325112865,-0.3826834323650903 L -0.9569403357322086,-0.2902846772544632 L -0.9807852804032302,-0.19509032201612947 L -1.9807852804032304,4.804909677983872 L -1.995184726672197,4.90198285967044 L -2.0,5.0 L -1.995184726672197,5.09801714032956 L -1.9807852804032304,5.195090322016128 L -1.9569403357322088,5.290284677254462 L -1.923879532511287,5.38268343236509 L -1.8819212643483554,5.471396736825997 L -1.8314696123025458,5.555570233019601 L -1.7730104533627378,5.634393284163645 L -1.7071067811865488,5.707106781186546 L -1.634393284163647,5.773010453362736 L -1.5555702330196042,5.831469612302544 L -1.4713967368260001,5.881921264348354 L -1.3826834323650925,5.923879532511286 L -1.2902846772544656,5.956940335732208 L -1.195090322016132,5.9807852804032295 L -1.0980171403295647,5.995184726672196 L -1.0000000000000044,6.0 L 5.0,6.0 L 5.098017140329561,5.995184726672197 L 5.195090322016128,5.98078528040323 L 5.290284677254462,5.956940335732209 L 5.38268343236509,5.923879532511287 L 5.471396736825998,5.881921264348355 L 5.555570233019602,5.831469612302545 L 5.634393284163646,5.773010453362737 L 5.707106781186548,5.707106781186548 L 5.773010453362737,5.634393284163646 L 5.831469612302545,5.555570233019602 L 5.881921264348355,5.471396736825998 L 5.923879532511287,5.38268343236509 L 5.956940335732209,5.290284677254462 L 5.98078528040323,5.195090322016128 L 5.995184726672197,5.09801714032956 L 6.0,5.0 L 5.995184726672197,4.901982859670439 L 5.98078528040323,4.804909677983871 L 5.956940335732209,4.709715322745537 L 5.923879532511286,4.6173165676349095 L 5.881921264348355,4.528603263174001 L 5.831469612302545,4.444429766980397 L 5.773010453362736,4.365606715836353 L 5.707106781186548,4.292893218813452 L 0.7071067811865475,-0.7071067811865475 L 0.6343932841636444,-0.7730104533627379 L 0.5555702330196012,-0.8314696123025459 L 0.4713967368259966,-0.8819212643483556 L 0.3826834323650888,-0.9238795325112872 L 0.29028467725446144,-0.9569403357322092 L 0.19509032201612744,-0.9807852804032307 L 0.09801714032955988,-0.9951847266721969 L -6.049014748177263e-16,-1.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeffa07790>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convex hull is the smallest convex polygon with contains all the points in the objects\n",
    "buffered_line.convex_hull\n",
    "# convex hull can be thought of the shape that a rubber band would make if you wrapped it around the outside of the object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "HKIoDpokejqI",
    "outputId": "55387792-f5db-4d3e-9080-9bb27e2b0e7d"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"0.8320000000000001 -31.368 20.535999999999998 36.936\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-25.799999999999997)\"><g><circle cx=\"2.2\" cy=\"4.2\" r=\"1.1080800000000002\" stroke=\"#555555\" stroke-width=\"0.36936\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"7.2\" cy=\"-25.1\" r=\"1.1080800000000002\" stroke=\"#555555\" stroke-width=\"0.36936\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"9.26\" cy=\"-2.456\" r=\"1.1080800000000002\" stroke=\"#555555\" stroke-width=\"0.36936\" fill=\"#66cc99\" opacity=\"0.6\" /><circle cx=\"20.0\" cy=\"-30.0\" r=\"1.1080800000000002\" stroke=\"#555555\" stroke-width=\"0.36936\" fill=\"#66cc99\" opacity=\"0.6\" /></g></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.multipoint.MultiPoint at 0x7feeff817250>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# can work on points also\n",
    "point4 = Point(20,-30)\n",
    "MultiPoint([point1, point2, point3, point4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "DgDCY7lcfjOu",
    "outputId": "5e8fbea7-5a54-413d-e542-dbffffee0aed"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"0.8320000000000001 -31.368 20.535999999999998 36.936\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-25.799999999999997)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.73872\" opacity=\"0.6\" d=\"M 20.0,-30.0 L 7.2,-25.1 L 2.2,4.2 L 9.26,-2.456 L 20.0,-30.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff817390>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MultiPoint([point1, point2, point3, point4]).convex_hull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "-uTr_9ixe8VS",
    "outputId": "ecd28cf4-1dc0-44f9-a988-1e4e2a8f731d"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"0.8320000000000001 -31.368 20.535999999999998 36.936\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-25.799999999999997)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.73872\" opacity=\"0.6\" d=\"M 2.2,-30.0 L 20.0,-30.0 L 20.0,4.2 L 2.2,4.2 L 2.2,-30.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff7e9c90>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# envelope finds the smallest upright rectangle that contains the object\n",
    "MultiPoint([point1, point2, point3, point4]).envelope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "jzkfqkKzfevw",
    "outputId": "6be37e89-6b5a-49e4-cd88-30b4bf0046e7"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-4.9526813335302835 -35.26151559647518 26.528552164280224 42.548512430248465\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,-27.974518762701887)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.8509702486049693\" opacity=\"0.6\" d=\"M -3.3768105027803403,2.0254812372981106 L 10.547728172519935,-33.685644765725236 L 20.0,-30.0 L 6.075461324699727,5.711126003023347 L -3.3768105027803403,2.0254812372981106 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff868690>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# minimum_rotated_rectangle allows for tilted rectangles\n",
    "MultiPoint([point1, point2, point3, point4]).minimum_rotated_rectangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "id": "aHtcR2S5f0tk",
    "outputId": "35b16768-6dc0-4e08-dae4-031af427ba64"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fda2414e450>]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parallel_offset creates a linestring that's a fixed distance from an object on left or right side\n",
    "original_line = LineString([(0,0),(5,5),(-1,5)])\n",
    "offset_line_left = original_line.parallel_offset(1,'left')\n",
    "offset_line_right_round = original_line.parallel_offset(1,'right',join_style=1)\n",
    "offset_line_right_sharp = original_line.parallel_offset(2,'right',join_style=2)\n",
    "offset_line_right_flat = original_line.parallel_offset(3,'right',join_style=3)\n",
    "plt.plot(original_line.xy[0], original_line.xy[1],'black')\n",
    "plt.plot(offset_line_left.xy[0], offset_line_left.xy[1],'red')\n",
    "plt.plot(offset_line_right_round.xy[0], offset_line_right_round.xy[1],'blue')\n",
    "plt.plot(offset_line_right_sharp.xy[0], offset_line_right_sharp.xy[1],'#AA33FF')\n",
    "plt.plot(offset_line_right_flat.xy[0], offset_line_right_flat.xy[1],'#33AAFF')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cVqYrJ7lhWzP"
   },
   "source": [
    "Join styles are documented [here](https://shapely.readthedocs.io/en/latest/manual.html#shapely.geometry.JOIN_STYLE)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BA1SIS6Eiga_"
   },
   "source": [
    "### Affine transformations\n",
    "You can perform arbitrary linear transformations of objects (scale, skew, translate, rotate) using the `affine_transform` function\n",
    "\n",
    "\n",
    "\n",
    "`affine_transform(geom, matrix_params)` transforms the object geom using the below matrix.\n",
    "$\\begin{split}\\begin{bmatrix}\n",
    "  x' \\\\\n",
    "  y' \\\\\n",
    "  1\n",
    "\\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "  a & b & x_\\mathrm{off} \\\\\n",
    "  d & e & y_\\mathrm{off} \\\\\n",
    "  0 & 0 & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "  x \\\\\n",
    "  y \\\\\n",
    "  1\n",
    "\\end{bmatrix}\\end{split}$\n",
    "\n",
    " Where `matrix_params` is a 6-tuple or list with entries\n",
    "`[a, b, d, e, x_off, y_off]`\n",
    "where:\n",
    "- `a` represents the scaling factor in the x direction\n",
    "- `b` represents the shearing factor in the x direction\n",
    "- `d` represents the shearing factor in the y direction\n",
    "- `e` represnts the scaling factor in the y direction\n",
    "- `x_off` represents the offset (translation) amount in the x direction\n",
    "- `y_off` represents the offset (translation) amount in the y direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UcMwFi0VjHfP"
   },
   "outputs": [],
   "source": [
    "from shapely.affinity import affine_transform, rotate, skew, scale, translate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "N3689DAtjqlC"
   },
   "source": [
    "`affine_transform` is very powerful, but it can be complicated to figure out the parameters by hand. Fortunately, common transformations have built-in functions:\n",
    "- [rotate](https://shapely.readthedocs.io/en/latest/manual.html#shapely.affinity.rotate)\n",
    "- [scale](https://shapely.readthedocs.io/en/latest/manual.html#shapely.affinity.scale)\n",
    "- [skew](https://shapely.readthedocs.io/en/latest/manual.html#shapely.affinity.skew)\n",
    "- [translate](https://shapely.readthedocs.io/en/latest/manual.html#shapely.affinity.translate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "2luh8t5TjrCu",
    "outputId": "68879d0a-7b34-43f4-f9c1-fb31c5925e22"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-0.08 -0.08 1.1600000000000001 2.16\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,2.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.0432\" opacity=\"0.6\" d=\"M 0.0,0.0 L 1.0,0.0 L 1.0,2.0 L 0.0,2.0 L 0.0,0.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff817690>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rect = Polygon([(0,0),(1,0),(1,2),(0,2)])\n",
    "rect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "ZznSV4QbsSqq",
    "outputId": "a5103f20-7c19-4481-bccc-96aa1d87cc0a"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-0.6455129855222069 -0.14551298552220704 2.291025971044414 2.291025971044414\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,2.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.04582051942088828\" opacity=\"0.6\" d=\"M 0.8535533905932737,-0.060660171779821304 L 1.5606601717798214,0.6464466094067262 L 0.14644660940672638,2.0606601717798214 L -0.5606601717798212,1.353553390593274 L 0.8535533905932737,-0.060660171779821304 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff861c50>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#rotate square by 45 degrees counter-clockwise (right hand rule determines direction)\n",
    "rotate(rect,45) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "DOuJCsfwsV4p"
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"100.0\" height=\"100.0\" viewBox=\"-1.1199999999999999 -0.12 3.24 2.24\" preserveAspectRatio=\"xMinYMin meet\"><g transform=\"matrix(1,0,0,-1,0,2.0)\"><path fill-rule=\"evenodd\" fill=\"#66cc99\" stroke=\"#555555\" stroke-width=\"0.06480000000000001\" opacity=\"0.6\" d=\"M -0.9999999999999999,0.0 L 1.1102230246251565e-16,0.0 L 2.0,2.0 L 0.9999999999999999,2.0 L -0.9999999999999999,0.0 z\" /></g></svg>"
      ],
      "text/plain": [
       "<shapely.geometry.polygon.Polygon at 0x7feeff861490>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skew(rect, 45)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DbqVTa8wss86"
   },
   "source": [
    "The usage for skew is:\n",
    "\n",
    "`shapely.affinity.skew(geom, xs=0.0, ys=0.0, origin='center', use_radians=False)`\n",
    "\n",
    "where `xs` is the skew in the x direct, and `ys` is in the y direction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wbyp8QS7ne-Q"
   },
   "source": [
    "# Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ouuSmdSenmaq"
   },
   "source": [
    "## Visualizing hurricane cone of uncertainty\n",
    "\n",
    "This is a common way of visualizing the possible hurricane paths. Thousands of simulations are run to forecast where the hurricane might be for each time step in the future. The larger circles the further out into the future we go represent the greater uncertainty about where the hurricane might be (not the actual size or power of the hurricane).\n",
    "\n",
    "![hurricane cone](https://www.weathernationtv.com/app/uploads/2016/10/C-Path-e1475672445449.jpg)\n",
    "\n",
    "In this exercise, you'll be given a set of forecasted locations for each time step in the future. Your job is to create an object that joins them together to create this style of continuous cone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "id": "eJicVDEDkn_h",
    "outputId": "6100e17c-bdda-4b3b-d1a3-ce0501502ac9"
   },
   "outputs": [
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      ],
      "text/plain": [
       "<shapely.geometry.multipolygon.MultiPolygon at 0x7feeff861450>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecast1 = Point(0,0).buffer(0.3)\n",
    "forecast2 = Point(-1,1.3).buffer(0.5)\n",
    "forecast3 = Point(-2.2,2.4).buffer(1)\n",
    "forecast4 = Point(-2.5,4.6).buffer(1.5)\n",
    "forecast5 = Point(-1,8.1).buffer(2.2)\n",
    "forecast6 = Point(3,8.5).buffer(2.6)\n",
    "\n",
    "all_forecasts = MultiPolygon([forecast1,\n",
    "                              forecast2,\n",
    "                              forecast3,\n",
    "                              forecast4,\n",
    "                              forecast5,\n",
    "                              forecast6])\n",
    "i = 0\n",
    "while i < (len(all_forecasts) - 2):\n",
    "    MultiPolygon([all_forecasts[i]])\n",
    "    i += 1\n",
    "for point in all_forecasts:\n",
    "    \n",
    "all_forecasts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8xOoXITQraJA"
   },
   "source": [
    "## Creating common logos\n",
    "Many logos and designs are made of simple geometric shapes. For example, Twitter's is entirely made from circles of different diameters.\n",
    "![alt text](https://shkspr.mobi/blog/wp-content/uploads/2017/05/TwitterCircles.jpg)\n",
    "\n",
    "Find an interesting logo that can be made with geometric shapes. Create it using shapely and plot it using matplotlib. As a bonus, try to match the colors as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZVTECCzUsCgl"
   },
   "outputs": [],
   "source": []
  }
 ],
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   "version": "0.3.2"
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