{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Try this yourself](https://colab.research.google.com/github/DTUWindEnergy/TopFarm2/blob/master/docs/notebooks/constraints.ipynb) (requires google account)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constraints are the second key element of an optimization problem formulation and they ensure that the optimization results represent feasible/realistic solutions. There are three types of constraints in optimization:\n",
    "\n",
    "- **Variable bounds**: upper and lower boundary values for design variables.\n",
    "- **Inequality constraints**: constraint function values must be less or more than a given threshold.\n",
    "- **Equality constraints**: constraint function must be exactly equal to a value (not as commonly used).\n",
    "\n",
    "In TOPFARM, the two most common type of constraints are boundary (`XYBoundaryConstraint`) and spacing constraints (`SpacingConstraint`). The boundaries constraints restrict the wind farm within a defined region, where the turbines inside are not allowed to cross this boundary and any exclusion zone must be avoided. In addition, spacing constraints tell TOPFARM the minimum allowable inter-turbine spacing in the farm.\n",
    "\n",
    "There is also the possibility of specifying additional constraints, such as fatigue loading or AEP. To do this, the **post_constraints** option in the TOPFARM problem is specified. More on how to set this up can be seen in the [load constrained layout optimization](https://topfarm.pages.windenergy.dtu.dk/TopFarm2/basic_examples_nblinks/layout_and_loads_nb.html) and [wake steering with load constraints](https://topfarm.pages.windenergy.dtu.dk/TopFarm2/advanced_examples_nblinks/wake_steering_and_loads_nb.html) examples.\n",
    "\n",
    "This notebook walks through a process to set up typical constraints in TOPFARM for wind farm design problems. Before working through the two types of boundaries, you must first import some basic libraries and functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make sure that you import or install topfarm on your newly created environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install TopFarm if needed\n",
    "import importlib\n",
    "if not importlib.util.find_spec(\"topfarm\"):\n",
    "    !pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/TopFarm2.git"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Import supporting libraries in Python**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import numpy and matplotlib files\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Next we import and initialize several functions and classes from TOPFARM to set up the problem including:**\n",
    "\n",
    "- **TopFarmProblem**. Overall topfarm problem class to which the objectives, design variables, and constraints are added\n",
    "- **XYPlotComp**. A helper function that shows the evolution of the optimization and the results at each iteration\n",
    "- **XYBoundaryConstraint**. For a boundary specified as a series of connected perimeter vertices\n",
    "- **CircleBoundaryConstraint**. For a circular boundary with a central location and a radius\n",
    "- **SpacingConstraint**. For the inter-turbine spacing distance constraints\n",
    "- **CostModelComponent**. A generic class for setting up a problem objective function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import topfarm problem, plotting support, constraint classes and generic cost model component\n",
    "from topfarm import TopFarmProblem\n",
    "from topfarm.plotting import XYPlotComp\n",
    "from topfarm.constraint_components.boundary import XYBoundaryConstraint, CircleBoundaryConstraint\n",
    "from topfarm.constraint_components.spacing import SpacingConstraint\n",
    "from topfarm.cost_models.cost_model_wrappers import CostModelComponent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boundary constraints\n",
    "\n",
    "Next we are going to demonstrate the use of the `XYBoundaryConstraint` to set up site boundaries of a variety of types including square, rectangle and an arbitrary polygon.  Additionally, a \"convex hull\" example is provided which is a commonly used boundary type for wind farm design optimization problems.\n",
    "\n",
    "**Convex hull**\n",
    "\n",
    "\"In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X.\" [[1]](https://en.wikipedia.org/wiki/Convex_hull)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up a \"boundary\" array with arbitrary points for use in the example\n",
    "boundary = np.array([(0, 0), (1, 1), (3, 0), (3, 2), (0, 2)])\n",
    "\n",
    "# set up dummy design variables and cost model component. \n",
    "# This example includes 2 turbines (n_wt=2) located at x,y=0.5,0.5 and 1.5,1.5 respectively\n",
    "\n",
    "x = [0.5,1.5]\n",
    "y = [.5,1.5]\n",
    "dummy_cost = CostModelComponent(input_keys=[],\n",
    "                                n_wt=2,\n",
    "                               cost_function=lambda : 1)   \n",
    "\n",
    "# We introduce a simple plotting function so we can quickly plot different types of site boundaries\n",
    "def plot_boundary(name, constraint_comp):\n",
    "    tf = TopFarmProblem(\n",
    "        design_vars={'x':x, 'y':y}, # setting up the turbine positions as design variables\n",
    "        cost_comp=dummy_cost, # using dummy cost model\n",
    "        constraints=[constraint_comp], # constraint set up for the boundary type provided\n",
    "        plot_comp=XYPlotComp()) # support plotting function\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(name)\n",
    "    tf.plot_comp.plot_constraints() # plot constraints is a helper function in topfarm to plot constraints\n",
    "    plt.plot(boundary[:,0], boundary[:,1],'.r', label='Boundary points') # plot the boundary points\n",
    "    plt.axis('equal')\n",
    "    plt.legend() # add the legend\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have set up our dummy problem, we can illustrate how different boundary types can be created from our boundary vertices. \n",
    "\n",
    "First we show a **convex hull** type as described above. Note that for the convex hull, all boundary points are contained within a convex perimeter but one of the boundary points on the interior is not used. When using the `XYBoundaryConstraint` in an optimization problem, TOPFARM uses convex hull as the default boundary type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary('convex_hull', XYBoundaryConstraint(boundary, 'convex_hull'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we show a **square** type of boundary. In this case the maximum distance between the x and y elements of the vertices is used to establish the perimeter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary('square', XYBoundaryConstraint(boundary, 'square'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now a **rectangle** boundary. Here we use the maximum distance on both x and y axes of the boundary coordinates to establish the perimeter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary('rectangle', XYBoundaryConstraint(boundary, 'rectangle'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, a **polygon** boundary, which connects all the points in sequence. Note that this results in a nonconvex boundary. Nonconvex functions in optimization problems introduce complexity that can be challenging to handle and often require more sophisticated algorithms and higher computational expense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary('polygon', XYBoundaryConstraint(boundary, 'polygon'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, a **circular** boundary, where the midpoint of the circle and the radius are specified by the user. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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o27dvhR/ndWTSizveNFBOTg6sra2RnZ0NKysr0XGIiIR69uwZrl69ikaNGlX4lO1U9SRJgqurK8LCwjB16tRXLnvgwAH4+PggKysLtWrVqp6AleRVr0dVP7+NqjokERGRvrl37x42bNiAjIyM1x5bhFhGiIiIKp2trS3q1auHyMhI1K5dW3QcjccyQkREVMnUnQHRvXv3qj3CqYbjBFYiIiISimWEiEhL6fP/SZPmqIzXoVplJDw8HB07doSlpSVsbW3Rv39/lQ7PGxUVhebNm8PMzAytW7fGjh07KhyYiEjflRzgSvTp6okA4MmTJwBePtKrOtSaM3Lw4EFMnDgRHTt2RFFREWbMmIHevXsjNTW1zMPhAsDRo0fxwQcfIDw8HP369cP69evRv39/JCUllXmK5Wp16xZw8eLzczRU0wF/iIjelJGRESwsLHDv3j0YGxvD4MVzzBCpo6Dg+cXE5PlFRZIk4cmTJ7h79y5q1apV4aPAAm94nJF79+7B1tYWBw8eRLdu3cpcZsiQIcjLy8P27duV13Xp0gXu7u5YsmSJSo9TJccZWbHif6fPNjB4fo4GAYdCJiKqiIKCAly9elWtc60QvSQ3F3jw4H+/160L1Kyp1ipq1aoFe3t7yGSyl26rluOMZGdnA3h+ZsHyHDt27KWDvfj6+mLr1q3l3ic/Px/5+fnK33Nyct4k5stu3fpfEQGe/xw/HvD15QgJUSV49uwZ0tPTlZcHDx6gsLAQRUVFyp9/vxgYGMDIyEh5MTY2Vv67Ro0ayiN2Ojg4oE6dOmW+6ekbExMTuLq6clcNVVxGBuDv/7/PQuD5CRPj4wF7e5VWYWxs/EYjIiUqXEYUCgUmT54MLy+vV+5uycjIUJ5PoISdnR0yMjLKvU94eDi+/fbbikZ7vYsXS298ACguBi5dYhkheoUnT54oC8adO3de+nfJzxdPNy6TyWBsbFyqZJRcDA0NIUlSqXLyYmH5O1NTU9jb28PR0VFZUEr+/ffr6tatq/O7LwwMDHgEVqq4q1efX1507RrQsGG1RqlwGZk4cSLOnTuHw4cPV2YeAMD06dNLjabk5OTA2dm58h7A1fX5rpkX26CLS+U9BpEWUygUuHTpEhITE5WX06dPv1QyzMzMShWBli1bllkOateuXeHRjGfPniEjI6Pc8nPo0CGkp6fj/v37pe5nbGwMFxcXeHh4oEOHDvDw8IC7uztqqjkETaSzNOizsEJl5KOPPsL27dtx6NAhOL1mJMHe3h6ZmZmlrsvMzIT9K4aATE1NYWpqWpFoqnFyej5HZPz45yMihobA0qUcFSG9VFbxSEpKUu4ebdiwITw8PPDPf/4TDRo0KFUyrK2tq3yXiZmZGRo2bIiGr/k/tYKCglKl5c6dO0hNTUVCQgKioqKQn58PmUyG5s2bs6AQARr1WajWBFZJkvDxxx8jOjoaBw4cgKur62vvM2TIEDx58gQxMTHK67p27Yo2bdqIncAKPJ87cunS8xbIIkJ6QNXi8fdL3bp1Bad+c4WFhUhNTVU+54SEBJw+fZoFhQio0s9CVT+/1SojYWFhWL9+PbZt24ZmzZopr7e2toa5uTkAIDg4GG+99RbCw8MBPP9qr7e3N+bMmQN/f39s2LABP/zwg1pf7eVZe4kq7unTp4iPj4dcLkdMTIxyvpauFg9VvaqgGBkZwdvbG4GBgQgICECjRo1ExyXSSlVSRsobjl21ahVGjhwJ4Pnx9Rs2bIjVq1crb4+KisKXX36Ja9euwdXVFf/+97/h5+en6sOyjBCpKTMzE9u3b0dMTAx2796Np0+fwtXVFYGBgejVqxc6dOigV8VDVSUF5fDhw9i+fTv27duHgoICtGrVCoGBgQgMDETHjh11fmIsUWWpkjIiCssI0atJkoTU1FTI5XLI5XKcOHECMpkMXbt2VX6I/n00k1Tz+PFj7N69G3K5HLGxsXjw4AHs7OwQEBCAgIAA9OzZExYWFqJjEmkslhEiHVdYWIg//vhDWUCuXr2KGjVqwNfXF4GBgfDz84ONjY3omDqjuLgYx44dU27vtLQ0mJmZoVevXggMDES/fv1eOTGfSB+xjBDpqISEBERERGDLli3Izs7GW2+9pRz96N69O487UU3S0tIQExMDuVyOI0eOQKFQoEuXLggNDcUHH3zAERMisIwQ6ZSnT59i48aNiIiIwKlTp1C/fn2MHDkSQUFBaNeuHY9IKtiDBw+wY8cObNiwAXFxcbC2tsbIkSMxYcIENG3aVHQ8ImFYRoh0wKVLl7BkyRKsXLkSWVlZ6NOnD8LCwuDn51cph2Cmynf16lUsXboUK1aswP3799GzZ0+EhYUhICAARkZvdAYOIq2j6uc3p4QTaZji4mLI5XL06dMHrq6uWLVqFcaMGYNLly4hLi4OAQEBLCIarFGjRpgzZw5u3ryJX3/9FXl5eRgwYAAaNmyI2bNnIz09XXREIo3DkREiDZGZmYkVK1Zg6dKluHHjBjp16oSwsDAMHjxYeRwf0k7JyclYvHgx1q1bh4KCAgwYMABhYWHo1q0bd7GRTuNuGiItIEkSjh49ikWLFmHTpk0wNDTEsGHDMGHCBHTo0EF0PKpkjx49wtq1axEREYG0tDS0bNkSYWFhCA4OhqWlpeh4RJWOu2mINNypU6fQs2dPvP322zh16hTmzp2L27dvY8WKFSwiOqpWrVr45JNPcOHCBcTHx6NFixaYNGkSGjVqhJ9++gnPnj0THZFICJYRomqWlpaGQYMGoVOnTsjMzMTWrVuRlpaGKVOmoE6dOqLjUTWQyWTo0aMHNm3ahKtXr2LAgAH47LPP0KxZM6xevRrFxcWiIxJVK5YRompy+/ZtjB07Fm5ubjh16hRWr16N06dPIygoiIcX12POzs6IjIzEuXPn0LFjR4waNQpt27aFXC6HFuxFJ6oUfAckqmIPHz7E559/DhcXF0RHR+PHH39EWloaQkJC+K0YUmrevDk2bdqEkydPws7ODkFBQXj77bfxxx9/iI5GVOVYRoiqyJMnTzBnzhw0adIEixYtwmeffYYrV65gypQpPEoqlatjx47Yu3cvdu3ahadPn6Jbt27o168fzpw5IzoaUZVhGSGqZIWFhVi6dClcXFwwc+ZMDB8+HJcvX8asWbP4bTBSiUwmQ+/evZGQkIANGzYgLS0N7u7uGDFiBK5evSo6HlGlYxkhqiSSJCEqKgpubm748MMP4ePjgz///BMLFy6EnZ2d6HikhQwMDDBkyBCkpqZi0aJF2Lt3L5o1a4ZPPvkE9+7dEx2PqNKwjBBVgtu3b6Nfv34YPHgwXFxckJycjHXr1qFx48aio5EOMDY2xoQJE3Dp0iV88803WLNmDVq0aIGNGzdykivpBJYRojcgSRJWrVoFNzc3JCcnQy6XY8eOHXB3dxcdjXRQjRo1MGPGDFy8eBE+Pj4YOnQo3n//fdy9e1d0NKI3wjJCVEEloyGjR49GUFAQzp8/j4CAANGxSA/Y2toiKioKGzduxMGDB9GyZUuOkpBWYxkhUlNZoyFr1qxB7dq1RUcjPTN48GCcP38e3bt35ygJaTWWESI1cDSENI2trS02bdqkHCVxc3PD77//LjoWkVpYRohUIEkSVq9erRwNiYmJ4WgIaZSSURJvb28MGTKEoySkVVhGiF6jZDRk1KhRytGQfv36iY5F9JK/j5IcOHCAoySkNVhGiMrB0RDSVhwlIW3DMkJUhidPnmDYsGEcDSGt9eIoSZs2bXD06FHRsYjKxDJC9IKbN2/inXfegVwux++//87RENJqgwcPxrlz5+Dq6gofHx+sWrVKdCSil7CMEP3N0aNH0bFjR9y/fx9HjhzB+++/LzoS0Ruzs7NDfHw8goODMXr0aEyZMgVFRUWiYxEpsYwQ/X+rVq2Cj48PmjZtilOnTvEoqqRTTExMEBkZiYULF2LhwoXw8/NDVlaW6FhEAFhGiFBUVIQpU6Zg9OjRCAkJwd69e2Frays6FlGlk8lk+Oijj7B7924kJiaiU6dOuHDhguhYRCwjpN+ysrLg5+eHhQsX4pdffsHSpUthYmIiOhZRlerRowdOnjwJU1NTdO7cGbGxsaIjkZ5jGSG9deHCBXTq1AmJiYnYvXs3Jk6cCJlMJjoWUbVo0qQJjh07Bh8fHwQEBGDu3Lk8tw0JwzJCeik2NhadO3eGqakpTp06hR49eoiORFTtLC0tER0djRkzZmDatGkYPnw4nj59KjoW6SGWEdIrkiRh7ty5CAgIgI+PD44dO4bGjRuLjkUkjIGBAb777jts2LAB0dHR6NatG27fvi06FukZlhHSG4WFhQgJCcG0adPwxRdfIDo6GpaWlqJjEWmEIUOG4PDhw8jIyECHDh2QnJwsOhLpEZYR0gv5+fkYPHgwNmzYgP/+97+YPXs2DAz48if6u/bt2yMhIQHOzs7o0aMHTpw4IToS6Qm+G5POe/r0Kd577z3ExcUhOjoaQ4cOFR2JSGPZ2dlh7969cHNzQ69evXD48GHRkUgPsIyQTsvLy0NAQAAOHDiA7du3w9/fX3QkIo1nZWWFnTt3okOHDvD19cW+fftERyIdxzJCOuvx48fo27cvTpw4gZ07d6Jnz56iIxFpjZo1ayI2NhbvvPMO/P39sXPnTtGRSIexjJBOys7ORu/evXH69Gns3r0b3bp1Ex2JSOuYm5tj27Zt6N27N4KCgiCXy0VHIh3FMkI6p2REJC0tDfv27YOnp6foSERay9TUFJs2bUJgYCAGDRqEHTt2iI5EOohlhHTKkydP0K9fP5w/fx67du2Ch4eH6EhEWs/Y2Bjr16+Hn58fBgwYgPj4eNGRSMewjJDOePbsGfr374/ExETs2LEDHTt2FB2JSGcYGxtj48aNysPHHzp0SHQk0iEsI6QTCgoKMGjQIPzxxx/Yvn07vLy8REci0jmmpqbYsmULPD094e/vj+PHj4uORDqCZYS0XlFRET744APs2bMH27ZtQ/fu3UVHItJZ5ubmkMvlcHd3R58+fZCUlCQ6EukAlhHSapIkYeLEiZDL5di0aRN69+4tOhKRzqtRowZiY2PRrFkz+Pr64tq1a6IjkZZjGSGtFhERgcjISCxduhQBAQGi4xDpDSsrK+zYsQOWlpYICgpCbm6u6EikxVhGSGvt27cPkyZNwqRJkzB69GjRcYj0Tt26dSGXy3HlyhWMHDkSCoVCdCTSUiwjpJWuXLmC999/Hz4+Ppg3b57oOER6q1WrVvjtt9+wefNmzJ49W3Qc0lIsI6R1Hj9+jMDAQNSpUwcbN26EkZGR6EhEei0oKAjfffcdvvnmG2zevFl0HNJCfBcnraJQKDBixAjcuHEDJ06cQJ06dURHIiIAM2bMwJkzZxAcHAwXFxe0bdtWdCTSIhwZIa3y9ddfQy6XY/369WjRooXoOET0/8lkMqxcuRLNmjVDUFAQ7t27JzoSaRGWEdIaGzduxHfffYfw8HD069dPdBwiekGNGjWwdetWPH36FIMGDUJBQYHoSKQlWEZIKyQlJWHUqFEYNmwY/vWvf4mOQ0TlqF+/PrZs2YJjx47hk08+ER2HtATLCGm8zMxM9O/fH25ubli+fDlkMpnoSET0Cl5eXli8eDGWLl2KxYsXi45DWoATWEmj5efnY8CAASgsLER0dDTMzc1FRyIiFYwZMwZnzpzBJ598gubNm8PHx0d0JNJgHBkhjfbJJ58gISEB0dHRcHJyEh2HiNQwf/58dO/eHe+//z6uX78uOg5pMJYR0lixsbGIjIzEL7/8gi5duoiOQ0RqMjIywsaNG2FhYYHQ0FBIkiQ6EmkolhHSSFlZWRg7diz69u2L0NBQ0XGIqILq1KmD5cuXY+/evYiMjBQdhzQUywhppClTpuDJkyeIjIzkhFUiLde7d2+Ehobi008/5e4aKhPLCGmc2NhYrFmzBj/99BPniRDpiPnz56N27drcXUNlYhkhjVKye8bPzw8jR44UHYeIKomVlRV311C5WEZIo0yePJm7Z4h0VO/evTF27Fh8+umnuHbtmug4pEFYRkhjbN++HWvXrsVPP/2Et956S3QcIqoC8+bN4+4aegnLCGmErKwsjBs3jrtniHRcye6a+Ph47q4hJZYR0gjcPUOkP7i7hl7EMkLCleye+fnnn7l7hkhPcHcN/Z3aZeTQoUMICAiAo6MjZDIZtm7d+srlDxw4AJlM9tIlIyOjoplJh/x990xISIjoOERUTbi7hv5O7TKSl5eHtm3bYtGiRWrdLy0tDenp6cqLra2tug9NOoi7Z4j0F3fXUAm1z9rbt29f9O3bV+0HsrW1Ra1atdS+H+muY8eOYe3atVi+fDl3zxDpqXnz5mHHjh34/PPPsXHjRtFxSJBqmzPi7u4OBwcH9OrVC0eOHHnlsvn5+cjJySl1Id0iSRKmTZuGNm3aYNSoUaLjEJEgVlZWmDVrFn7//XckJiaKjkOCVHkZcXBwwJIlS7B582Zs3rwZzs7O6N69O5KSksq9T3h4OKytrZUXZ2fnqo5J1Wznzp04dOgQwsPDYWDAedRE+iw4OBgtWrTA9OnTRUchQWTSG0xjlslkiI6ORv/+/dW6n7e3N+rXr49ff/21zNvz8/ORn5+v/D0nJwfOzs7Izs6GlZVVReOShlAoFGjfvj2srKxw8OBBzhUhIkRHR2PAgAHYu3cv3n33XdFxqJLk5OTA2tr6tZ/fas8ZqQydOnXC4cOHy73d1NQUpqam1ZiIqtOGDRtw+vRpHD16lEWEiAAA/fv3R5cuXTBt2jScPHmS7w16Rsj4eEpKChwcHEQ8NAlWUFCAr776CkFBQfD09BQdh4g0hEwmw5w5c5CQkIDNmzeLjkPVTO2RkdzcXFy6dEn5+9WrV5GSkoI6deqgfv36mD59Om7fvo21a9cCAH7++Wc0atQIbm5uePbsGZYvX459+/Zh9+7dlfcsSGtERkbi2rVrkMvloqMQkYbx9vZGnz598MUXX6B///4wMhIyeE8CqD0ykpCQgHbt2qFdu3YAgKlTp6Jdu3aYOXMmACA9PR03btxQLl9QUIB//vOfaN26Nby9vXH69GnuE9RTubm5mD17NoKDg+Hm5iY6DhFpoPDwcPz1119YtWqV6ChUjd5oAmt1UXUCDGm22bNn47vvvsNff/2FBg0aiI5DRBpq2LBhOHjwIC5evAgLCwvRcegNqPr5ze9UUrW4d+8efvzxR0ycOJFFhIheafbs2bh79y4WLlwoOgpVE5YRqhbh4eEAgBkzZghOQkSarkmTJhg/fjzmzJmDrKws0XGoGrCMUJW7fv06Fi1ahM8++wz16tUTHYeItMCXX36JgoICzJ07V3QUqgYsI1TlvvnmG9SqVQtTpkwRHYWItIS9vT2mTp2KBQsW4Pbt26LjUBVjGaEqdevWLfz666+YMWMGatasKToOEWmRTz/9FKamppw7ogdYRqhKLVu2DObm5jwZHhGpzdraGqNGjcKKFSvw7Nkz0XGoCrGMUJUpLCxEZGQkRowYwa9kE1GFfPjhh7h//z42bdokOgpVIZYRqjJbt25FRkYGJkyYIDoKEWmpZs2aoWfPnoiIiBAdhaoQywhVmYiICLzzzjto3bq16ChEpMXCwsJw7NgxJCcni45CVYRlhKpEamoqDhw4gLCwMNFRiEjLBQQE4K233sLixYtFR6EqwjJCVWLx4sWwtbXFgAEDREchIi1nZGSE8ePHY926dXj06JHoOFQFWEao0uXm5mLNmjUYO3YsTExMRMchIh0QGhqKgoIC5RnhSbewjFClW7duHfLy8jBu3DjRUYhIRzg4OGDAgAGIiIiAFpzfldTEMkKVSpIkREREICAgAPXr1xcdh4h0SFhYGNLS0rB//37RUaiSsYxQpTp69CjOnDnDiatEVOm6deuGli1b8mu+OohlhCpVREQEXFxc0LNnT9FRiEjHyGQyhIWFYevWrTxfjY5hGaFKc/fuXURFRWHChAkwMOBLi4gq34gRI2BmZoZly5aJjkKViJ8YVGlWr14NQ0NDjBw5UnQUItJRVlZWGDFiBCIjI1FcXCw6DlUSlhGqNFu2bIG/vz/q1KkjOgoR6bDhw4cjPT0dJ0+eFB2FKgnLCFWKjIwMnDhxAoGBgaKjEJGO69KlC+rVqwe5XC46ClUSlhGqFNu3b4eBgQH8/PxERyEiHWdoaIh+/fqxjOgQlhGqFHK5HF5eXqhXr57oKESkBwIDA5GamorLly+LjkKVgGWE3tiTJ0+wZ88e7qIhomrTq1cvmJqaIiYmRnQUqgQsI/TG4uPj8ezZMwQEBIiOQkR6ombNmujRowd31egIlhF6Y3K5HE2bNkWzZs1ERyEiPRIYGIhDhw4hKytLdBR6Qywj9EYUCgViYmK4i4aIql2/fv1QXFyMuLg40VHoDbGM0Bs5deoUMjMzWUaIqNo5OTnBw8OD80Z0AMsIvRG5XI66devC09NTdBQi0kOBgYGIi4tDQUGB6Cj0BlhG6I3I5XL4+fnByMhIdBQi0kMBAQHIzs7GH3/8IToKvQGWEaqwK1eu4Ny5c9xFQ0TCuLu7w8nJid+q0XIsI1RhMTExMDExga+vr+goRKSnZDIZAgMDIZfLIUmS6DhUQSwjVGHbt29H9+7dYWlpKToKEemxwMBAXLt2DampqaKjUAWxjFCFKBQKnDhxAj4+PqKjEJGee+edd2BgYIBjx46JjkIVxDJCFXLx4kU8fvwYHh4eoqMQkZ6zsLBAixYtkJiYKDoKVRDLCFVIyR99+/btBSchIgI8PDyQkJAgOgZVEMsIVUhiYiIaNmyIunXrio5CRAQPDw+cOXOGxxvRUiwjVCEJCQno0KGD6BhERACADh06oKCgAOfPnxcdhSqAZYTUplAokJyczPkiRKQx3N3dYWBgwHkjWoplhNTGyatEpGk4iVW7sYyQ2jh5lYg0ESexai+WEVIbJ68SkSbiJFbtxTJCaktMTOTkVSLSOJzEqr1YRkgtCoUCSUlJnC9CRBqHk1i1F8sIqYWTV4lIU3ESq/ZiGSG1cPIqEWkyTmLVTiwjpBZOXiUiTcZJrNqJZYTUkpqaijZt2oiOQURUpjZt2qCgoABXrlwRHYXUwDJCarlz5w6cnJxExyAiKlPJ+9OdO3cEJyF1sIyQWtLT0+Hg4CA6BhFRmUren9LT0wUnIXWwjJDKCgoKcO/ePTg6OoqOQkRUpho1asDKyoplRMuwjJDKMjMzAYAjI0Sk0RwcHLibRsuwjJDKSv64WUaISJM5ODhwZETLsIyQykr+uLmbhog0maOjI0dGtAzLCKksPT0dRkZGqFevnugoRETl4siI9mEZIZXduXMH9vb2MDDgy4aINJejoyPLiJbhpwqpjF/rJSJt4ODggNzcXDx+/Fh0FFIRywip7M6dOywjRKTxeKwR7cMyQipLT0/n5FUi0ngl71OcxKo9WEZIZRwZISJtwJER7cMyQiopLCzk0VeJSCtYWlqiZs2aLCNahGWEVJKZmQlJkjgyQkRagUdh1S4sI6SSnJwcAECtWrXEBiEiUkGtWrWU71uk+VhGSCVFRUUAAGNjY8FJiIhez9jYWPm+RZqPZYRUUvJHbWRkJDgJEdHrGRkZsYxoEZYRUgnLCBFpEyMjIxQWFoqOQSpSu4wcOnQIAQEBcHR0hEwmw9atW197nwMHDqB9+/YwNTWFi4sLVq9eXYGoJBJ306jp1i1g//7nP4mo2nE3jXZRu4zk5eWhbdu2WLRokUrLX716Ff7+/vDx8UFKSgomT56M0NBQ7Nq1S+2wJA5HRtSwYgXQoAHQo8fznytWiE5EpHe4m0a7qP3J0rdvX/Tt21fl5ZcsWYJGjRph/vz5AIAWLVrg8OHD+Omnn+Dr61vmffLz85Gfn6/8nTOixSsZ7mQZeY1bt4Bx4wCF4vnvCgUwfjzg6ws4OYnNRqRHWEa0S5XPGTl27Bh69uxZ6jpfX18cO3as3PuEh4fD2tpaeXF2dq7qmPQaxcXFAABDQ0PBSTTcxYv/KyIliouBS5fE5CHSU4aGhiwjWqTKy0hGRgbs7OxKXWdnZ4ecnBw8ffq0zPtMnz4d2dnZysvNmzerOia9RsmISEkpoXK4ugIGL/xZGRoCLi5i8hDpqeLiYo7kahGN/DaNqakprKysSl1IrJI/av6fxms4OQGRkc8LCPD859Kl3EVDVM2KiopYRrRIlf+Xsre3R2ZmZqnrMjMzYWVlBXNz86p+eKokJX/U/KqcCsaMeT5H5NKl5yMiLCJE1a6wsJCfMVqkysuIp6cnduzYUeq6PXv2wNPTs6ofmioRR0bU5OTEEkIkUFFREQ9FoEXU3k2Tm5uLlJQUpKSkAHj+1d2UlBTcuHEDwPP5HsHBwcrlP/zwQ1y5cgX/+te/8OeffyIiIgK///47pkyZUjnPgKoFywgRaRPuptEuapeRhIQEtGvXDu3atQMATJ06Fe3atcPMmTMBAOnp6cpiAgCNGjVCbGws9uzZg7Zt22L+/PlYvnx5uV/rJc3E3TREpE0KCwtZRrSI2v+lunfvDkmSyr29rKOrdu/eHcnJyeo+FGkQlhEi0iYcGdEuGvltGtI81tbWAIBHjx6JDUJEpIKsrCzl+xZpPpYRUomdnR1kMhnS09NFRyEieiVJkpCeng5HR0fRUUhFLCOkEiMjI9ja2uLOnTuioxARvdLjx4+Rl5cHBwcH0VFIRSwjpDJHR0eOjBCRxit5n+LIiPZgGSGVOTg4cGSEiDReyfsUR0a0B8sIqYwjI0SkDUrep1hGtAfLCKnMwcGBZYSINF56ejosLS1Rs2ZN0VFIRSwjpDJHR0dkZGTwzL1EpNHu3LnDUREtwzJCKnNwcEBxcTHu378vOgoRUbn4tV7twzJCKiv54+YkViLSZBwZ0T4sI6Sykj9uzhshIk2Wnp7OMqJlWEZIZSVHYeXICBFpsjt37nA3jZZhGSGVGRsbw8bGhiMjRKSxcnNzkZuby5ERLcMyQmrh13uJSJPxGCPaiWWE1OLo6IibN2+KjkFEVKZbt24B4KHgtQ3LCKnFzc0NZ86cER2DiKhMp0+fhqmpKRo3biw6CqmBZYTU0qFDB9y4cYPHGiEijZSYmAh3d3cYGxuLjkJqYBkhtXh4eAB4/gdPRKRpEhMTle9TpD1YRkgtTZo0gbW1NcsIEWmc3Nxc/PnnnywjWohlhNQik8nQvn17JCQkiI5CRFRKcnIyJEliGdFCLCOkNg8PD46MEJHGSUxMhKmpKVq2bCk6CqmJZYTU5uHhwUmsRKRxOHlVe7GMkNo4iZWINBEnr2ovlhFSW5MmTWBlZcUyQkQag5NXtRvLCKnNwMAAHh4enMRKRBqDk1e1G8sIVQgnsRKRJuHkVe3GMkIVwkmsRKRJOHlVu7GMUIVwEisRaRJOXtVuLCNUISWTWDlvhIhE4+RV7ccyQhViYGAAT09P7N+/X3QUItJzBw8ehCRJ8PT0FB2FKohlhCosICAABw8eRHZ2tugoRKTHYmJi4OLigubNm4uOQhXEMkIVFhAQgKKiIuzcuVN0FCLSUwqFAjExMQgMDIRMJhMdhyqIZYQqrH79+nB3d4dcLhcdhYj0VFJSEu7cuYOAgADRUegNsIzQGwkMDMSOHTtQWFgoOgoR6SG5XI7atWvDy8tLdBR6Aywj9EYCAgLw6NEjHD58WHQUItJDcrkcfn5+PL6IlmMZoTfSvn17ODo6IiYmRnQUItIzN27cwOnTpxEYGCg6Cr0hlhF6IwYGBggICIBcLockSaLjEJEeiYmJgbGxMXx9fUVHoTfEMkJvLDAwEJcvX8aFCxdERyEiPSKXy+Ht7Q1ra2vRUegNsYzQG+vRowcsLCz4rRoiqjY5OTnYv38/d9HoCJYRemNmZmbw9fVlGSGiarNr1y4UFhbyK706gmWEKkVgYCCOHz+Ou3fvio5CRHpALpejTZs2aNiwoegoVAlYRqhS+Pv7AwBiY2MFJyEiXVdUVIQdO3ZwF40OYRmhSmFjY4OuXbti27ZtoqMQkY47evQoHj58yDKiQ1hGqNIMGDAAcXFxuHfvnugoRKTD1q5dC2dnZ3h4eIiOQpWEZYQqTUhICGQyGVauXCk6ChHpqKysLKxfvx7jx4+HgQE/wnQF/0tSpalbty6GDh2KJUuWoLi4WHQcItJBa9asQVFREcaMGSM6ClUilhGqVGFhYbh27Rp27twpOgoR6RiFQoGIiAgMHDgQ9vb2ouNQJWIZoUrVsWNHeHh4ICIiQnQUItIx+/btw8WLFxEWFiY6ClUylhGqVDKZDGFhYYiLi8OVK1dExyEiHRIREYFWrVrh7bffFh2FKhnLCFW6oUOHwtraGkuXLhUdhYh0xK1bt7Bt2zaEhYVBJpOJjkOVjGWEKp2FhQVGjRqFFStW4NmzZ6LjEJEOiIyMhIWFBYYPHy46ClUBlhGqEh9++CEePHiAqKgo0VGISMsVFBRg2bJlCA4OhqWlpeg4VAVYRqhKNG3aFL169eJEViJ6Y1u3bkVGRgYmTJggOgpVEZYRqjJhYWE4fvw4kpKSREchIi0WERGBbt26oVWrVqKjUBVhGaEq069fPzg5OWHx4sWioxCRljp//jwOHjzIr/PqOJYRqjJGRkYYP3481q1bh0ePHomOQ0RaaPHixbCzs8N7770nOgpVIZYRqlKhoaEoLCzEsmXLREchIi3z8OFDrF27FmPHjoWJiYnoOFSFWEaoStnb22PUqFGYO3cusrOzRcchIi0yd+5cKBQKfPTRR6KjUBVjGaEq9/XXXyMvLw/z5s0THYWItMStW7fwf//3f5g6dSrs7OxEx6EqxjJCVe6tt97CpEmT8J///AcZGRmi4xCRFvj2229Ro0YNfPrpp6KjUDVgGaFq8fnnn8PExATfffed6ChEpOH+/PNPrFy5El988QWsrKxEx6FqwDJC1aJ27dqYNm0ali5disuXL4uOQ0Qa7Msvv4STkxMPcqZHWEao2nz88cewtbXFzJkzRUchIg116tQpbN68GbNmzYKZmZnoOFRNWEao2lhYWODrr7/G+vXrkZKSIjoOEWkYSZIwbdo0uLm58YR4eqZCZWTRokVo2LAhzMzM0LlzZ5w8ebLcZVevXg2ZTFbqwrarv0aPHo2mTZtixowZoqMQkYbZu3cv9u3bhx9++AGGhoai41A1UruMbNy4EVOnTsXXX3+NpKQktG3bFr6+vrh7926597GyskJ6errycv369TcKTdrLyMgI33//PeLi4nDw4EHRcYhIQygUCkybNg1du3ZFQECA6DhUzdQuI//5z38wduxYjBo1Ci1btsSSJUtgYWGBlStXlnsfmUwGe3t75YXfGddvAwcORIcOHfD5559DkiTRcYhIA0RFRSEpKQlz5syBTCYTHYeqmVplpKCgAImJiejZs+f/VmBggJ49e+LYsWPl3i83NxcNGjSAs7MzgoKCcP78+Vc+Tn5+PnJyckpdSHfIZDLMmTMHJ06cwLZt20THISLBCgsL8eWXX8Lf3x/vvPOO6DgkgFpl5P79+yguLn5pZMPOzq7cg1k1a9YMK1euxLZt2/Dbb79BoVCga9euuHXrVrmPEx4eDmtra+XF2dlZnZikBd5991306tULM2bMQFFRkeg4RCTQihUrcPnyZYSHh4uOQoJU+bdpPD09ERwcDHd3d3h7e2PLli2wsbHB0qVLy73P9OnTkZ2drbzcvHmzqmOSAOHh4bhw4QIiIyNFRyEiQbKysvDNN99g+PDhaN26teg4JIhaZaRevXowNDREZmZmqeszMzNhb2+v0jqMjY3Rrl07XLp0qdxlTE1NYWVlVepCusfDwwPjxo3D559/jmvXromOQ0QCTJ48Gc+ePeOoiJ5Tq4yYmJjAw8MD8fHxyusUCgXi4+Ph6emp0jqKi4tx9uxZODg4qJeUdNKPP/6IOnXqIDQ0lJNZifRMTEwM1q5diwULFuCtt94SHYcEUns3zdSpU7Fs2TKsWbMGFy5cwIQJE5CXl4dRo0YBAIKDgzF9+nTl8rNmzcLu3btx5coVJCUlYfjw4bh+/TpCQ0Mr71mQ1rKyssKKFSsQHx//yl13RKRbsrKyMH78ePj7+yM4OFh0HBLMSN07DBkyBPfu3cPMmTORkZEBd3d37Ny5Uzmp9caNGzAw+F/HycrKwtixY5GRkYHatWvDw8MDR48eRcuWLSvvWZBW69mzJ8aNG4fPPvsMffr0QcOGDUVHIqIqNmnSJDx58gRLly7lV3kJMkkLxsZzcnJgbW2N7Oxszh/RUTk5OWjdujVcXFywd+9evjkR6bCYmBgEBgZi9erVCAkJER2HqpCqn988Nw1phJLdNfv27ePuGiIdxt0zVBaWEdIYf99dw2/XEOkm7p6hsrCMkEYp+XbNmDFjoFAoRMchokoUExODX3/9ld+eoZewjJBG+fvuGh4MjUh3PHz4EOPGjePuGSoTywhpHO6uIdI9kydPxtOnT7l7hsrEMkIaibtriHQHd8/Q67CMkEb6++6aRYsWiY5DRBV09+5dfnuGXotlhDRWz5498cknn2Dq1Kk4ePCg6DhEpKaCggIMHDgQCoUCkZGR3D1D5WIZIY02b948dOvWDQMHDsTVq1dFxyEiFUmShIkTJ+LkyZOIjo6Go6Oj6EikwVhGSKMZGxvj999/h7W1NYKCgpCbmys6EhGpYNGiRVi+fDmWLFmi8olUSX+xjJDGq1u3LuRyOa5evYrg4GBOaCXScPv27cPkyZMxZcoU5UlUiV6FZYS0gpubG9atW4etW7di1qxZouMQUTkuX76M999/Hz169MC///1v0XFIS7CMkNYIDAzEd999h2+//RabNm0SHYeIXpCTk4PAwEDUqVMHGzduhJGR2ieGJz3FVwpplenTp+PMmTMICQmBi4sL3N3dRUciIgAKhQLDhw/HrVu3cPz4cdSuXVt0JNIiHBkhrSKTybBy5Uo0b94cQUFBuHv3ruhIRARg5syZ2L59O/773/+iRYsWouOQlmEZIa1jYWGBrVu3Ij8/H4MGDUJBQYHoSER6bePGjfj+++8xd+5c+Pn5iY5DWohlhLSSs7MztmzZghMnTuCjjz6CJEmiIxHppcTERIwaNQrDhw/Hp59+KjoOaSmWEdJaXbt2xeLFi7Fs2TIeMp5IgIyMDPTv3x+tWrXiEVbpjXACK2m10aNH4+zZs5g0aRJsbW0xePBg0ZGI9MLDhw/Rp08fFBcXIzo6Gubm5qIjkRZjGSGtN2/ePNy/fx/Dhg2DqakpgoKCREci0mnZ2dnw9fXF7du3ceDAAZ6Jl94Yd9OQ1jM0NMSqVaswYMAAvP/++4iLixMdiUhn5ebmws/PD5cuXcKePXvg5uYmOhLpAJYR0glGRkZYt24d+vbtiwEDBiA+Pl50JCKd8+TJEwQEBODs2bPYvXs3j/NDlYZlhHRGyUn1vL29ERgYiD/++EN0JCKd8ezZM7z33ns4deoU4uLi0LFjR9GRSIewjJBOMTU1xZYtW9C5c2f4+fnh8OHDoiMRab1nz55h4MCBOHToEGJiYuDl5SU6EukYlhHSORYWFpDL5ejQoQN8fX2xb98+0ZGItFZeXh4CAgKwf/9+yOVy+Pj4iI5EOohlhHRSzZo1ERsbi7fffhv+/v7YuXOn6EhEWufx48fw8/PDsWPHEBcXh169eomORDqKZYR0loWFBbZt24ZevXohKCgIcrlcdCQirfHo0SP07t0bKSkp2L17N7y9vUVHIh3GMkI6zczMDJs2bUJAQAAGDhyIqKgo0ZGINN6DBw/w7rvvIi0tDfHx8ejatavoSKTjWEZI55mYmGDDhg0YPHgwhg4diuXLl4uORKSxbty4AR8fH9y4cQP79+9Hhw4dREciPcAjsJJeMDIywtq1a2FtbY2xY8fi3LlzmDdvHoyM+CdAVOLIkSMYMGAAzM3NcfDgQbRs2VJ0JNITHBkhvWFoaIiIiAhERETgl19+Qd++ffHw4UPRsYg0wooVK+Dj44PmzZvj1KlTLCJUrVhGSO9MmDABe/bsQVJSEjp16oTU1FTRkYiEKSoqwqRJkxAaGopRo0Zhz549sLGxER2L9AzLCOklHx8fnDp1Cubm5ujSpQu2b98uOhJRtXv48CH69u2LRYsWYdGiRViyZAlMTExExyI9xDJCeqtx48Y4evQoevTogcDAQMydOxeSJImORVQtUlNT0alTJyQlJWHPnj0ICwuDTCYTHYv0FMsI6TVLS0ts2bIFX3zxBaZNm4bhw4fj6dOnomMRVamYmBh06dIF5ubmOHXqFI+qSsKxjJDeMzAwwOzZs7Fx40ZER0fjnXfewa1bt0THIqp0kiRhzpw5CAoKQo8ePXD06FE0btxYdCwilhGiEoMHD8aRI0dw9+5ddOzYEcePHxcdiajSPHnyBP/4xz8wffp0fPHFF9iyZQssLS1FxyICwDJCVEq7du1w6tQpNGnSBN7e3li1ahXnkZDWu3HjBrp164atW7di48aNmD17NgwM+PZPmoOvRqIX2NnZIT4+HsHBwRg9ejQGDRqEzMxM0bGI1CZJElasWIHWrVvj7t27OHLkCAYPHiw6FtFLWEaIymBqaoply5YhKioKf/zxB9zc3LBhwwaOkpDWuHnzJvz8/BAaGooBAwbg9OnTaNeunehYRGViGSF6hUGDBuH8+fN499138cEHH3CUhDReyWhIq1atcObMGWzfvh2rVq1C7dq1RUcjKhfLCNFr2NjYYOPGjRwlIY1369atUqMh586dg7+/v+hYRK/FMkKkIo6SkKaSJAkrV66Em5sbR0NIK7GMEKmBoySkaUpGQ8aMGcPRENJaLCNEFcBREhKNoyGkS1hGiCqIoyQkCkdDSNewjBC9oRdHSby9vXH06FHRsUgHPXr0CDNmzEDTpk05GkI6hWWEqBKUjJLExcUhJycHXl5eCAoKwvnz50VHIx3w9OlTzJs3D40bN8aCBQswZcoUpKamcjSEdAbLCFEl6tOnD5KSkrBu3TqcO3cOrVu3xsiRI3H9+nXR0UgLFRUVYcWKFWjatCmmT5+OoUOH4tKlS/j+++9hbW0tOh5RpWEZIapkBgYGGDZsGC5cuICFCxciLi4OTZs2xZQpU3D//n3R8UgLSJKELVu2oHXr1ggNDcXbb7+NCxcuICIiAg4ODqLjEVU6lhGiKmJiYoKJEyfi8uXL+Oqrr7BixQo0btwYs2fPRm5uruh4pKH279+PLl26YODAgahfvz4SExPx3//+Fy4uLqKjEVUZlhGiKlazZk18+eWXuHLlCkJDQ/Hdd9+hSZMm+OWXX1BQUCA6HmmI5ORk9OnTBz169AAAxMfHY9euXWjfvr3gZERVj2WEqJrUq1cP//nPf3Dx4kX4+flh0qRJaN68OX777TcUFRWJjkeCpKWl4YMPPkD79u1x7do1bN68GcePH1eWEiJ9wDJCVM3q16+PVatW4cyZM2jTpg1GjBiBhg0bYtasWUhPTxcdj6pBUVERtm3bBl9fXzRv3hx//PEHli1bhnPnzmHAgAGQyWSiIxJVK5YRIkHc3NywdetWpKSkwN/fH3PnzkX9+vUxePBgHDhwgAdP00GZmZn4/vvv0bhxY/Tv3x/Z2dlYs2YNLl26hNDQUBgZGYmOSCSETNKCd7ycnBxYW1sjOzsbVlZWouMQVYns7GysXbsWERER+PPPP9GiRQuEhYVhxIgR/BqnFpMkCYcPH0ZERAQ2b94MIyMjDBs2DBMmTICHh4foeERVStXPb5YRIg0jSRIOHDiAiIgIREdHw8zMDMOHD0dYWBjatGkjOh6p6PHjx/jtt98QERGBc+fOwdXVFWFhYQgJCeERU0lvsIwQ6YDbt29j2bJliIyMRHp6Ory8vBAWFoaBAwfC1NRUdDwqw7lz57B48WKsXbsWT548QVBQEMLCwtCjRw8YGHDPOOkXlhEiHVJYWIht27YhIiIC+/fvh42NDYYPH46goCB4eXlxroFgN2/eRExMDDZs2IA//vgDdnZ2GDt2LMaNGwdnZ2fR8YiEYRkh0lGpqalYsmQJoqKikJGRgdq1a8Pf3x+BgYHw9fXl30g1kCQJSUlJkMvlkMvlSElJgZGREby9vTF27Fi89957MDExER2TSDiWESIdp1AokJCQALlcjpiYGJw5cwbGxsbo3r07AgMDERAQgAYNGoiOqTOePXuGffv2ISYmBjExMbh9+zasra3h5+eHwMBA9OnTB7Vq1RIdk0ijsIwQ6Zlr164hJiYGcrkcBw4cQFFREdq2bassJh4eHpyzoKZ79+4hNjYWcrkcu3fvRl5eHho1aoSgoCAEBATgnXfegbGxseiYRBqLZYRIj2VnZ2Pnzp2IiYlBbGwsHj16BAcHBwQEBKB3797o0KED6tevz4NrvSA3NxcpKSk4cuQIYmJicPToUQBA586dERgYiMDAQLRs2ZLbjUhFLCNEBOD55NcjR44o5zdcvnwZAFC3bl14eHjAw8MDHTp0gIeHh14VlJLikZiYqLxcuHABkiTB3NwcvXv3RmBgIPz9/WFnZyc6LpFWqtIysmjRIvz444/IyMhA27ZtsXDhQnTq1Knc5aOiovDVV1/h2rVrcHV1xdy5c+Hn56fy47GMEFWeO3fulPoATkxMVB6GXlcLyquKh6mpKdq0aaN8vh4eHnBzc+PuF6JKUGVlZOPGjQgODsaSJUvQuXNn/Pzzz4iKikJaWhpsbW1fWv7o0aPo1q0bwsPD0a9fP6xfvx5z585FUlISWrVqValPRm23bgEXLwKuroCTU+Wtl0jLpKenIzExEQkJCeUWlHbt2qFBgwZwcHCAo6MjHBwcYG9vrxEf2pIkISsrC+np6UhPT8edO3dw584dpKamvlQ82rZtqywdLB5EqNLPwiorI507d0bHjh3xyy+/AHg+o9/Z2Rkff/wxpk2b9tLyQ4YMQV5eHrZv3668rkuXLnB3d8eSJUsq9cmoZcUKYNw4QKEADAyAyEhgzJjKWTeRDigpKCWX06dP486dOy+dYdjGxkZZTkp+/v3fjo6OqFevHoyNjWFkZKTSKIskSVAoFCgqKkJubq6yYLzqZ35+fql11K5dG66urqVGelq2bMniQfR3VfxZWCVlpKCgABYWFti0aRP69++vvD4kJASPHj3Ctm3bXrpP/fr1MXXqVEyePFl53ddff42tW7fi9OnTZT5Ofn5+qTeWnJwcODs7V14ZuXULaNDg+cYvYWgIXLvGERKiV1AoFLh///5ry0FGRgYKCwvLXIehoSGMjIxKXUqKR8mlvPsCQJ06dV5bfuzt7WFubl5Vm4FIN1TDZ6GqZUStwzbev38fxcXFL03msrOzw59//lnmfTIyMspcPiMjo9zHCQ8Px7fffqtONPVcvFh64wNAcTFw6RLLCNErGBgYwNbWFra2tmjbtm25yykUCjx48EC52+T+/fulisaLxePFglIyimJkZAQLC4tSu4XMzMyq8RkT6TAN+izUyGNIT58+HVOnTlX+XjIyUmlcXZ8PR73YBl1cKu8xiPSYgYEBbGxsYGNjw5P7EWkqDfosVOsISPXq1YOhoSEyMzNLXZ+ZmQl7e/sy72Nvb6/W8gBgamoKKyurUpdK5eT0fL+YoeHz3w0NgaVLOSpCRET6Q4M+C9UqIyYmJvDw8EB8fLzyOoVCgfj4eHh6epZ5H09Pz1LLA8CePXvKXb7ajBnzfL/Y/v3Pf3LyKhER6RsN+SxUezfN1KlTERISgg4dOqBTp074+eefkZeXh1GjRgEAgoOD8dZbbyE8PBwAMGnSJHh7e2P+/Pnw9/fHhg0bkJCQgMjIyMp9JhXh5MTRECIi0m8a8FmodhkZMmQI7t27h5kzZyIjIwPu7u7YuXOncpLqjRs3Sp3/omvXrli/fj2+/PJLzJgxA66urti6davKxxghIiIi3cbDwRMREVGVUPXzm6fwJCIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgoI9EBVCFJEgAgJydHcBIiIiJSVcnndsnneHm0oow8fvwYAODs7Cw4CREREanr8ePHsLa2Lvd2mfS6uqIBFAoF7ty5A0tLS8hkskpbb05ODpydnXHz5k1YWVlV2np1EbeVeri9VMdtpTpuK9VxW6muKreVJEl4/PgxHB0dYWBQ/swQrRgZMTAwgJOTU5Wt38rKii9WFXFbqYfbS3XcVqrjtlIdt5XqqmpbvWpEpAQnsBIREZFQLCNEREQklF6XEVNTU3z99dcwNTUVHUXjcVuph9tLddxWquO2Uh23leo0YVtpxQRWIiIi0l16PTJCRERE4rGMEBERkVAsI0RERCQUywgREREJxTJCREREQul8GVm0aBEaNmwIMzMzdO7cGSdPnnzl8lFRUWjevDnMzMzQunVr7Nixo5qSiqfOtlq9ejVkMlmpi5mZWTWmFefQoUMICAiAo6MjZDIZtm7d+tr7HDhwAO3bt4epqSlcXFywevXqKs+pCdTdVgcOHHjpdSWTyZCRkVE9gQUKDw9Hx44dYWlpCVtbW/Tv3x9paWmvvZ8+vmdVZFvp63vW4sWL0aZNG+XRVT09PREXF/fK+4h4Tel0Gdm4cSOmTp2Kr7/+GklJSWjbti18fX1x9+7dMpc/evQoPvjgA4wZMwbJycno378/+vfvj3PnzlVz8uqn7rYCnh86OD09XXm5fv16NSYWJy8vD23btsWiRYtUWv7q1avw9/eHj48PUlJSMHnyZISGhmLXrl1VnFQ8dbdVibS0tFKvLVtb2ypKqDkOHjyIiRMn4vjx49izZw8KCwvRu3dv5OXllXsffX3Pqsi2AvTzPcvJyQlz5sxBYmIiEhIS0KNHDwQFBeH8+fNlLi/sNSXpsE6dOkkTJ05U/l5cXCw5OjpK4eHhZS4/ePBgyd/fv9R1nTt3lsaPH1+lOTWButtq1apVkrW1dTWl01wApOjo6Fcu869//Utyc3Mrdd2QIUMkX1/fKkymeVTZVvv375cASFlZWdWSSZPdvXtXAiAdPHiw3GX0+T3r71TZVnzP+p/atWtLy5cvL/M2Ua8pnR0ZKSgoQGJiInr27Km8zsDAAD179sSxY8fKvM+xY8dKLQ8Avr6+5S6vKyqyrQAgNzcXDRo0gLOz8yubtr7T19fVm3B3d4eDgwN69eqFI0eOiI4jRHZ2NgCgTp065S7D19ZzqmwrgO9ZxcXF2LBhA/Ly8uDp6VnmMqJeUzpbRu7fv4/i4mLY2dmVut7Ozq7c/c8ZGRlqLa8rKrKtmjVrhpUrV2Lbtm347bffoFAo0LVrV9y6das6ImuV8l5XOTk5ePr0qaBUmsnBwQFLlizB5s2bsXnzZjg7O6N79+5ISkoSHa1aKRQKTJ48GV5eXmjVqlW5y+nre9bfqbqt9Pk96+zZs6hZsyZMTU3x4YcfIjo6Gi1btixzWVGvKaMqXTvpLE9Pz1LNumvXrmjRogWWLl2K2bNnC0xG2qxZs2Zo1qyZ8veuXbvi8uXL+Omnn/Drr78KTFa9Jk6ciHPnzuHw4cOio2g8VbeVPr9nNWvWDCkpKcjOzsamTZsQEhKCgwcPlltIRNDZkZF69erB0NAQmZmZpa7PzMyEvb19mfext7dXa3ldUZFt9SJjY2O0a9cOly5dqoqIWq2815WVlRXMzc0FpdIenTp10qvX1UcffYTt27dj//79cHJyeuWy+vqeVUKdbfUifXrPMjExgYuLCzw8PBAeHo62bdtiwYIFZS4r6jWls2XExMQEHh4eiI+PV16nUCgQHx9f7r4yT0/PUssDwJ49e8pdXldUZFu9qLi4GGfPnoWDg0NVxdRa+vq6qiwpKSl68bqSJAkfffQRoqOjsW/fPjRq1Oi199HX11ZFttWL9Pk9S6FQID8/v8zbhL2mqnR6rGAbNmyQTE1NpdWrV0upqanSuHHjpFq1akkZGRmSJEnSiBEjpGnTpimXP3LkiGRkZCTNmzdPunDhgvT1119LxsbG0tmzZ0U9hWqj7rb69ttvpV27dkmXL1+WEhMTpaFDh0pmZmbS+fPnRT2FavP48WMpOTlZSk5OlgBI//nPf6Tk5GTp+vXrkiRJ0rRp06QRI0Yol79y5YpkYWEhffbZZ9KFCxekRYsWSYaGhtLOnTtFPYVqo+62+umnn6StW7dKFy9elM6ePStNmjRJMjAwkPbu3SvqKVSbCRMmSNbW1tKBAwek9PR05eXJkyfKZfie9VxFtpW+vmdNmzZNOnjwoHT16lXpzJkz0rRp0ySZTCbt3r1bkiTNeU3pdBmRJElauHChVL9+fcnExETq1KmTdPz4ceVt3t7eUkhISKnlf//9d6lp06aSiYmJ5ObmJsXGxlZzYnHU2VaTJ09WLmtnZyf5+flJSUlJAlJXv5Kvn754Kdk+ISEhkre390v3cXd3l0xMTKTGjRtLq1atqvbcIqi7rebOnSs1adJEMjMzk+rUqSN1795d2rdvn5jw1ays7QSg1GuF71nPVWRb6et71ujRo6UGDRpIJiYmko2NjfTuu+8qi4gkac5rSiZJklS1Yy9ERERE5dPZOSNERESkHVhGiIiISCiWESIiIhKKZYSIiIiEYhkhIiIioVhGiIiISCiWESIiIhKKZYSIiIiEYhkhIiIioVhGiIiISCiWESIiIhLq/wEjtTg3wFtqLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary('Circle',CircleBoundaryConstraint((1.5,1),1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a simple for loop we can quickly plot all boundary types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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0WaoCFi5cqCeeeEKjR4/Wxx9/rMzMTI0cObLUTao/DU6XDBkyRH5+fkpPT9fy5ct18eJF3X333RXedlXydBy8vb21du1affTRR+rQoYNmzZqluLg4HTp0qNpqJIwAQEM1erR0+HDJt2kOHy55XcMcDoe8vLx07tw5SVL79u31v//7v243S27evFleXl6Ki4uTVPKNkaysLNf84uLiUjd6Xk379u315Zdf6vz58662zz77zK3P5s2b1bt3b40bN05dunRRbGysvv322wqt38fHRykpKXrnnXf0zjvv6N57763Q7wj9tIbTp0/rm2++Ufv27V01b968uVSN7dq1k/elUOmhS2d0Lj+z4nA41KdPH02fPl27du2Sr6+v0tPTK7WNiiCMAEBDFhUl9etX7WdELikqKlJ2drays7O1b98+PfrooyooKNCQIUMkSffff7/8/f2VkpKiPXv2aP369Xr00Uf1wAMPKCwsTJI0YMAArVy5UitXrtTXX3+tsWPHevycjPvuu08Oh0MPPfSQ9u7dq1WrVumVV15x69O2bVtt375da9as0TfffKNnn33W7abUq3nwwQe1bt06rV69ukKXaCRpxowZysjI0J49ezRixAhdd911SkpKkiQ9/vjjysjI0B/+8Ad98803evfdd/XGG2+UuvHWE61bt5bD4dCKFSuUm5urgoICff7553rhhRe0fft2HT16VH/729+Um5vrCkXVgTACAKgxq1evVkREhCIiItSzZ0/XN2b69esnSQoICNCaNWv0z3/+U927d9fdd9+t2267TW+88YZrHaNGjVJKSoqGDx+uvn376mc/+5nrK6oVFRQUpOXLl2v37t3q0qWLfv/73+ull15y6/Pwww/rN7/5jZKTk9WzZ0/94x//0Lhx4yq8jbZt26p379668cYb1bNnzwot8+KLL+qxxx5Tt27dlJ2dreXLl7vOXnTt2lWLFy/WwoULdfPNN2vq1KmaMWOG21eaPRUZGanp06dr8uTJCgsL04QJExQcHKxNmzbpjjvuULt27fTMM89o5syZGjRoUKW3czUOc/mFt1ooPz9fISEhysvLU3BwsO1yAMCq8+fP69ChQ2rTpk2lf7Id1c8Yo7Zt22rcuHGaNGnSFftu2LBB/fv31+nTp9W0adOaKbCKXGl/rOjx26e6iwQAoKHJzc3VwoULlZ2dfdVni4AwAgBAlWvZsqWuu+46paWlqVmzZrbLqfUIIwAAVDFP74Do169f9T7htJbjBlYAAGAVYQQA6qiG/C9p1B5VsR96FEZSU1PVvXt3NWnSRC1btlRSUlKFHs+7ZMkS3XjjjfL391fHjh21atWqShcMAA3dpQdc2f65ekCSzp49K6n0k1494dE9Ixs3btT48ePVvXt3/fjjj3r66af1y1/+Unv37i3zcbiStGXLFg0bNkypqam68847tWDBAiUlJWnnzp1l/sRyjTp+XDpwoOQ3GmrogT8AcK18fHwUEBCg3NxcNWrUSF6X/8YM4IkLF0omX9+SqYKMMTp79qxOnTqlpk2bVvopsNI1PmckNzdXLVu21MaNG/WLX/yizD7JyckqLCzUihUrXG29evVS586dNXfu3Aptp1qeM/LWWzJjxsjhdMp4eenCrFn6MSWlatYNANXs4sWLOnnyJJdqcE0chYVy/POf/2po0UIKCvJoHU2bNlV4eLgcDkepeTXynJG8vDxJJb8sWJ6tW7eWethLYmKili1bVu4yRUVFKioqcr3Oz8+/ljJLO37cFUQkyeF0ynv8eN0wfrxOVO2WAKDa+Pj4KDw8/Jr+RYqGK0zSOklue4+3t5SRIYWHV2gdjRo1qpL9r9JhxOl0auLEierTp88VL7dkZ2e7fk/gkrCwMGVnZ5e7TGpqqqZPn17Z0q7uwAFXELnER1KsRBgBUGf8+OOPOn78uO0yUEe1kVTmDRaHD0sxMTVaS6XDyPjx47Vnzx59+umnVVmPJGnKlCluZ1Py8/MVHR1ddRto21bGy8stkBhvb63au1cmMrLqtgMAQC3lOHFCpn1793+ce3tLsbE1XkulwsiECRO0YsUKbdq0SVFXufEzPDxcOTk5bm05OTkKv8IpID8/P/n5+VWmtIqJitKFWbPkPX68fFQSRBzz5imgXbvq2yYAALVJu3YqKuNYaOMLHR7dgm2M0YQJE5Senq5169apTZs2V10mISFBGRkZbm1r165VQkKCZ5VWsR9TUhQjqZ+kc3v3SqNHW60HAICaVluOhR6dGRk/frwWLFigDz/8UE2aNHHd9xESEqLGjRtLkoYPH67IyEilpqZKkh577DH17dtXM2fO1ODBg7Vw4UJt375daWlpVfxWPHfi/ycuzQAAGqracCz06MzInDlzlJeXp379+ikiIsI1LVq0yNXn6NGjysrKcr3u3bu3FixYoLS0NMXHx+uDDz7QsmXL7D9jBAAA1ArX9JyRmlIdzxkpLCxU0P9/l7qgoKDch7YBAFBfVfexsKLHbx7bBwAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwyuMwsmnTJg0ZMkStWrWSw+HQsmXLrth/w4YNcjgcpabs7OzK1gwAAOoRj8NIYWGh4uPjNXv2bI+W279/v7KyslxTy5YtPd00AACoh3w8XWDQoEEaNGiQxxtq2bKlmjZt6vFyAACgfquxe0Y6d+6siIgI3X777dq8efMV+xYVFSk/P99tAgAA9VO1h5GIiAjNnTtXS5cu1dKlSxUdHa1+/fpp586d5S6TmpqqkJAQ1xQdHV3dZQIAAEscxhhT6YUdDqWnpyspKcmj5fr27avrr79e7733Xpnzi4qKVFRU5Hqdn5+v6Oho5eXlKTg4uLLluiksLFRQUJAkqaCgQIGBgVWyXgAA6orqPhbm5+crJCTkqsdvj+8ZqQo9evTQp59+Wu58Pz8/+fn51WBFAADAFivPGcnMzFRERISNTQMAgFrG4zMjBQUFOnjwoOv1oUOHlJmZqebNm+v666/XlClTdOLECf3Xf/2XJOm1115TmzZtdNNNN+n8+fN68803tW7dOn388cdV9y4AAECd5XEY2b59u/r37+96PWnSJElSSkqK5s+fr6ysLB09etQ1/8KFC3r88cd14sQJBQQEqFOnTvrkk0/c1gEAABqua7qBtaZU9AYYT3ADKwCgoastN7Dy2zQAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCqPw8imTZs0ZMgQtWrVSg6HQ8uWLbvqMhs2bFDXrl3l5+en2NhYzZ8/vxKlAnXI8ePS+vUlfwEAV+RxGCksLFR8fLxmz55dof6HDh3S4MGD1b9/f2VmZmrixIl68MEHtWbNGo+LBeqEt96SWreWBgwo+fvWW7YrAoBazWGMMZVe2OFQenq6kpKSyu3z1FNPaeXKldqzZ4+r7d5779UPP/yg1atXl7lMUVGRioqKXK/z8/MVHR2tvLw8BQcHV7ZcN4WFhQoKCpIkFRQUKDAwsErWiwbu+PGSAOJ0/qvN21s6fFiKirJWFgCUpbqPhfn5+QoJCbnq8bva7xnZunWrBg4c6NaWmJiorVu3lrtMamqqQkJCXFN0dHR1lwlUjQMH3IOIJBUXSwcP2qkHAOqAag8j2dnZCgsLc2sLCwtTfn6+zp07V+YyU6ZMUV5enms6duxYdZcJVI22bSWvy/5v5e0txcbaqQcA6oBa+W0aPz8/BQcHu01AnRAVJaWllQQQqeTvvHlcogGAK/Cp7g2Eh4crJyfHrS0nJ0fBwcFq3LhxdW8eqHmjR0uJiSWXZmJjCSIAcBXVHkYSEhK0atUqt7a1a9cqISGhujcN2BMVRQgBgAry+DJNQUGBMjMzlZmZKankq7uZmZk6evSopJL7PYYPH+7q/8gjj+i7777T7373O3399df685//rMWLF+s///M/q+YdAACAOs3jMLJ9+3Z16dJFXbp0kSRNmjRJXbp00dSpUyVJWVlZrmAiSW3atNHKlSu1du1axcfHa+bMmXrzzTeVmJhYRW8BAADUZdf0nJGaUtHvKXuC54wAABq6BvOcEQAAgCshjAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsKpSYWT27NmKiYmRv7+/evbsqW3btpXbd/78+XI4HG6Tv79/pQsGAAD1i8dhZNGiRZo0aZKmTZumnTt3Kj4+XomJiTp16lS5ywQHBysrK8s1HTly5JqKBgAA9YfHYeSPf/yjHnroIY0cOVIdOnTQ3LlzFRAQoLfffrvcZRwOh8LDw11TWFjYNRUNAADqD4/CyIULF7Rjxw4NHDjwXyvw8tLAgQO1devWcpcrKChQ69atFR0drbvuuktfffXVFbdTVFSk/Px8twkAANRPHoWR77//XsXFxaXObISFhSk7O7vMZeLi4vT222/rww8/1Pvvvy+n06nevXvr+PHj5W4nNTVVISEhrik6OtqTMgEAQB1S7d+mSUhI0PDhw9W5c2f17dtXf/vb3xQaGqp58+aVu8yUKVOUl5fnmo4dO1bdZQIAAEt8POl83XXXydvbWzk5OW7tOTk5Cg8Pr9A6GjVqpC5duujgwYPl9vHz85Ofn58npQEAgDrKozMjvr6+6tatmzIyMlxtTqdTGRkZSkhIqNA6iouLtXv3bkVERHhWKQAAqJc8OjMiSZMmTVJKSopuueUW9ejRQ6+99poKCws1cuRISdLw4cMVGRmp1NRUSdKMGTPUq1cvxcbG6ocfftDLL7+sI0eO6MEHH6zadwIAAOokj8NIcnKycnNzNXXqVGVnZ6tz585avXq166bWo0ePysvrXydcTp8+rYceekjZ2dlq1qyZunXrpi1btqhDhw5V9y4AAECd5TDGGNtFXE1+fr5CQkKUl5en4ODgKllnYWGhgoKCJJV89TgwMLBK1gsAQF1R3cfCih6/+W0aAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVlQojs2fPVkxMjPz9/dWzZ09t27btiv2XLFmiG2+8Uf7+/urYsaNWrVpVqWIBAED943EYWbRokSZNmqRp06Zp586dio+PV2Jiok6dOlVm/y1btmjYsGEaPXq0du3apaSkJCUlJWnPnj3XXPy1ipTUT5LjxAnLlQAAYEdtOBY6jDHGkwV69uyp7t2764033pAkOZ1ORUdH69FHH9XkyZNL9U9OTlZhYaFWrFjhauvVq5c6d+6suXPnVmib+fn5CgkJUV5enoKDgz0pt1znZ89WowkT5C3JeHnpwqxZ+jElpUrWDQBAXVCclqbASZNcx0JHWpo0enSVrb/Cx2/jgaKiIuPt7W3S09Pd2ocPH25+/etfl7lMdHS0efXVV93apk6dajp16lTuds6fP2/y8vJc07Fjx4wkk5eX50m55Tt2zDi9vIyRXNNFyURKRkxMTExMTA1gipTMj5LbsdB4extz7FjVHGuNMXl5eUa6+vHbo8s033//vYqLixUWFubWHhYWpuzs7DKXyc7O9qi/JKWmpiokJMQ1RUdHe1Lm1R04IIfT6dbkIym2arcCAECt1VaS9+WNxcXSwYM1XotPjW+xAqZMmaJJkya5Xufn51dtIGnbtuR01E8CifH21qq9e2UiI6tuOwAA1FKOEydk2rd3/8e5t7cUW/P/NPcojFx33XXy9vZWTk6OW3tOTo7Cw8PLXCY8PNyj/pLk5+cnPz8/T0rzTFRUyXWxhx8uSYHe3nLMm6eAdu2qb5sAANQm7dpJlx0LNW+eFBVV46V4dJnG19dX3bp1U0ZGhqvN6XQqIyNDCQkJZS6TkJDg1l+S1q5dW27/GjN6tHT4sLR+fcnfKrxhBwCAOqGWHAs9vkwzadIkpaSk6JZbblGPHj302muvqbCwUCNHjpQkDR8+XJGRkUpNTZUkPfbYY+rbt69mzpypwYMHa+HChdq+fbvS0tKq9p1URlSUlQQIAECtUQuOhR6HkeTkZOXm5mrq1KnKzs5W586dtXr1atdNqkePHpWX179OuPTu3VsLFizQM888o6efflpt27bVsmXLdPPNN1fduwAAAHWWx88ZsaE6njMCAACqV0WP3/w2DQAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArPKxXUBFGGMkSfn5+ZYrAQAAFXXpuH3pOF6eOhFGzpw5I0mKjo62XAkAAPDUmTNnFBISUu58h7laXKkFnE6nTp48qSZNmsjhcFTZevPz8xUdHa1jx44pODi4ytZbHzFWnmG8Ko6xqjjGquIYq4qrzrEyxujMmTNq1aqVvLzKvzOkTpwZ8fLyUlRUVLWtPzg4mJ21ghgrzzBeFcdYVRxjVXGMVcVV11hd6YzIJdzACgAArCKMAAAAqxp0GPHz89O0adPk5+dnu5Raj7HyDONVcYxVxTFWFcdYVVxtGKs6cQMrAACovxr0mREAAGAfYQQAAFhFGAEAAFYRRgAAgFWEEQAAYFW9DyOzZ89WTEyM/P391bNnT23btu2K/ZcsWaIbb7xR/v7+6tixo1atWlVDldrnyVjNnz9fDofDbfL396/Bau3ZtGmThgwZolatWsnhcGjZsmVXXWbDhg3q2rWr/Pz8FBsbq/nz51d7nbWBp2O1YcOGUvuVw+FQdnZ2zRRsUWpqqrp3764mTZqoZcuWSkpK0v79+6+6XEP8zKrMWDXUz6w5c+aoU6dOrqerJiQk6KOPPrriMjb2qXodRhYtWqRJkyZp2rRp2rlzp+Lj45WYmKhTp06V2X/Lli0aNmyYRo8erV27dikpKUlJSUnas2dPDVde8zwdK6nk0cFZWVmu6ciRIzVYsT2FhYWKj4/X7NmzK9T/0KFDGjx4sPr376/MzExNnDhRDz74oNasWVPNldrn6Vhdsn//frd9q2XLltVUYe2xceNGjR8/Xp999pnWrl2rixcv6pe//KUKCwvLXaahfmZVZqykhvmZFRUVpRdffFE7duzQ9u3bNWDAAN1111366quvyuxvbZ8y9ViPHj3M+PHjXa+Li4tNq1atTGpqapn9hw4dagYPHuzW1rNnT/Pwww9Xa521gadj9c4775iQkJAaqq72kmTS09Ov2Od3v/uduemmm9zakpOTTWJiYjVWVvtUZKzWr19vJJnTp0/XSE212alTp4wks3HjxnL7NOTPrJ+qyFjxmfUvzZo1M2+++WaZ82ztU/X2zMiFCxe0Y8cODRw40NXm5eWlgQMHauvWrWUus3XrVrf+kpSYmFhu//qiMmMlSQUFBWrdurWio6OvmLQbuoa6X12Lzp07KyIiQrfffrs2b95suxwr8vLyJEnNmzcvtw/7VomKjJXEZ1ZxcbEWLlyowsJCJSQklNnH1j5Vb8PI999/r+LiYoWFhbm1h4WFlXv9OTs726P+9UVlxiouLk5vv/22PvzwQ73//vtyOp3q3bu3jh8/XhMl1ynl7Vf5+fk6d+6cpapqp4iICM2dO1dLly7V0qVLFR0drX79+mnnzp22S6tRTqdTEydOVJ8+fXTzzTeX26+hfmb9VEXHqiF/Zu3evVtBQUHy8/PTI488ovT0dHXo0KHMvrb2KZ9qXTvqrYSEBLdk3bt3b7Vv317z5s3TH/7wB4uVoS6Li4tTXFyc63Xv3r317bff6tVXX9V7771nsbKaNX78eO3Zs0effvqp7VJqvYqOVUP+zIqLi1NmZqby8vL0wQcfKCUlRRs3biw3kNhQb8+MXHfddfL29lZOTo5be05OjsLDw8tcJjw83KP+9UVlxupyjRo1UpcuXXTw4MHqKLFOK2+/Cg4OVuPGjS1VVXf06NGjQe1XEyZM0IoVK7R+/XpFRUVdsW9D/cy6xJOxulxD+szy9fVVbGysunXrptTUVMXHx+v1118vs6+tfarehhFfX19169ZNGRkZrjan06mMjIxyr5UlJCS49ZektWvXltu/vqjMWF2uuLhYu3fvVkRERHWVWWc11P2qqmRmZjaI/coYowkTJig9PV3r1q1TmzZtrrpMQ923KjNWl2vIn1lOp1NFRUVlzrO2T1Xr7bGWLVy40Pj5+Zn58+ebvXv3mjFjxpimTZua7OxsY4wxDzzwgJk8ebKr/+bNm42Pj4955ZVXzL59+8y0adNMo0aNzO7du229hRrj6VhNnz7drFmzxnz77bdmx44d5t577zX+/v7mq6++svUWasyZM2fMrl27zK5du4wk88c//tHs2rXLHDlyxBhjzOTJk80DDzzg6v/dd9+ZgIAA8+STT5p9+/aZ2bNnG29vb7N69Wpbb6HGeDpWr776qlm2bJk5cOCA2b17t3nssceMl5eX+eSTT2y9hRozduxYExISYjZs2GCysrJc09mzZ119+MwqUZmxaqifWZMnTzYbN240hw4dMl9++aWZPHmycTgc5uOPPzbG1J59ql6HEWOMmTVrlrn++uuNr6+v6dGjh/nss89c8/r27WtSUlLc+i9evNi0a9fO+Pr6mptuusmsXLmyhiu2x5OxmjhxoqtvWFiYueOOO8zOnTstVF3zLn399PLp0vikpKSYvn37llqmc+fOxtfX1/zsZz8z77zzTo3XbYOnY/XSSy+ZG264wfj7+5vmzZubfv36mXXr1tkpvoaVNU6S3PYVPrNKVGasGupn1qhRo0zr1q2Nr6+vCQ0NNbfddpsriBhTe/YphzHGVO+5FwAAgPLV23tGAABA3UAYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFX/Bx3PoHBOsPv8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for boundary_type in ['convex_hull','square','rectangle','polygon']:\n",
    "    plot_boundary(boundary_type, XYBoundaryConstraint(boundary, boundary_type))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Exercise \n",
    "\n",
    "Play around with a new set of boundary vertices and construct different perimeters to explore the functionality. See if you can make even more complex polygon shapes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WVN4eRE2bNlVqaqpSU1PVp08fLVu2TKdPn9bSpUt9foyoqKgqtXx1P+W1YcOGXtddLpfcF+5Xa5Gbm6uHHnpIEydO1DvvvKNdu3Zp/PjxVU7QPD8EnXPTTTcpJiZGa9eu1RtvvKGzZ8/q17/+tc/PbSZ/X4fo6Ght3LhR69evV+fOnfXMM8+oU6dOOnDgQLBHBYJm/vz5nj+7g+6+W0pPD/rfd0Bt/A4WbrdbK1asUGZmpho0sNWPGvnZxImVid3C5O5yuRQVFaWffvpJkpSWlqa///3vXicKbt26VVFRUerUqZOkync+HDt2zPP1ioqKKic51iUtLU27d+/WmTNnPLd99NFHXsds3bpV1157rSZPnqwePXooNTVVX331lU+P36BBA2VmZmrFihVasWKFbr/9dp9+rsv5M5w8eVJffvml0tLSPDNv3bq1yoxXXHGFos8FRD+da1oubDxcLpf69++vuXPn6pNPPlGjRo20du3agJ4DsNq5tkKqPIH8pptusngiIIBg8e677+rw4cM+1d+WSk4OaXIvKytTYWGhCgsL9fnnn2vq1KkqLS31/EHPyMhQbGysMjMztXfvXuXl5Wnq1Km666671LJlS0nSoEGDtG7dOq1bt05ffPGF7r//fr8/h+HOO++Uy+XSvffeq88++0xvvfWW/vjHP3od07FjR+3YsUMbNmzQl19+qUcffdTrhMy63HPPPXrvvff09ttv+/z74PHHH9emTZu0d+9ejRs3TpdccolGjx4tSXrwwQe1adMmPfHEE/ryyy/1wgsvaNGiRVVOOvVHu3bt5HK59Oabb6qoqEilpaX629/+pnnz5mnHjh06fPiw/vd//1dFRUWegAM4zfltxbBhwxQfH2/xREAAwWLIkCEyDENXXHFFMOZxrLffflutW7dW69at1bdvX887P9LT0yVJTZo00YYNG/T999+rT58++vWvf63rr79eixYt8jzGhAkTlJmZqbvvvlsDBgzQZZdd5nnbpK8uuugivfHGG9qzZ4969Oihf/u3f9N//Md/eB1z33336Ve/+pVuu+029e3bV999950mT57s83N07NhR1157ra688kr17dvXp/vMnz9f06ZNU69evVRYWKg33njD0yr07NlTL730knJzc9WlSxc99thjevzxx+t8x1FtLr30Us2dO1czZ85Uy5YtNWXKFMXHx+v999/XiBEjdMUVV+h3v/udFixYoOHDhwf8PIBVzm8rJD6oEPbhMi5c6gdZSUmJEhISVFxcXCVdnzlzRgcOHFCHDh34MdU2ZhiGOnbsqMmTJ2vGjBm1Hrt582YNHDhQJ0+e1MUXXxyaAU3C70fYWVZWlp577jlJlWuQEydO0FggqGr7/n0+m54kAbsqKipSbm6uCgsL6/zsCgDBcWFbwRoEdkKwgF9atGihSy65RDk5OWrWrJnV4wAR6fxzKyTWILAXggX84u/mLD09nU+2BEx0YVvBu0FgNwF/pDcAIPQubCtYg8BubBks+Bcu7IDfh7CbC9sKiTUI7MdWweLchyFZ/SO6AUn68ccfJVX9hE/AKufainPnN7EGgR3Z6hyLBg0aqEmTJioqKlLDhg0VdeHP/ABCwDAM/fjjjzpx4oQuvvjigD/9EzDT+W3FVVddpb/+9a+sQWBLtgoWLpdLrVu31oEDBzw/vAuwysUXX6xWrVpZPQYg6ee24rrrrtPx48clsQaBPdkqWEiVP+OhY8eOrENgqYYNG9JUwDbObytuueUWTZs2jTUIbMt2wUKq/CmffNIhAFQ611YMGDBARUVFkng3COyLkxgAwMbObytmz56tl19+WRJrENgXwQIAbOz8tiIxMVH5+fmsQWBrBAsAsKnz24o5c+Z42grWILAzggUA2NT5bcWAAQNYg8ARbPVj0wEAlQoKCpSamqry8nLl5eWpefPm6tatGz8iHZbx9fs3jQUA2ND5bUV6ejprEDgGwQIAbObCcysMw2ANAscgWACAzVzYVuzZs4d3g8AxCBYAYCMXthWSWIPAUQgWAGAjF7YVrEHgNAQLALCJ6toK1iBwGoIFANjEhW2FxBoEzkOwAAAbqK6tYA0CJyJYAIANVNdWsAaBExEsAMBi1bUVEmsQOBPBAgAsVl1bwRoETkWwAAAL1dRWsAaBUxEsAMBC1bUVEmsQOBfBAgAsUlNbwRoETkawAACL1NRWsAaBkxEsAMACNbUVEmsQOBvBAgAsUFNbwRoETkewAIAQq62tYA0CpyNYAECI1dRWSKxB4HwECwAIodraCtYgCAcECwAIodraCtYgCAd+B4ujR49q7NixSkxMVOPGjXX11Vdrx44dwZgNAMJKbW2FxBoE4aGBPwefPHlS/fv318CBA7V+/XolJSVp3759atasWbDmA4CwUVtbwRoE4cJlGIbh68EzZ87U1q1b9cEHH/j8BGVlZSorK/NcLykpUUpKioqLi0nkACJGQUGBUlNTVV5erry8vCrBYvfu3erWrZtiYmJ04sQJ/n6E7ZSUlCghIaHO799+rUJef/119e7dW2PGjFGLFi3Uo0cPLV26tNb7ZGdnKyEhwXNJSUnx5ykBICzU1lZIrEEQPvxqLGJjYyVJM2bM0JgxY7R9+3ZNmzZNzz//vDIzM6u9D40FgEhXV1thGIbS0tKUn5+vlStXKiMjw5pBgVr42lj4dY6F2+1W7969NW/ePElSjx49tHfv3lqDRUxMjGJiYvx5GgAIK3W1FbwbBOHEr1VI69at1blzZ6/b0tLSdPjwYVOHAoBwUdc7QSTWIAgvfgWL/v37Kz8/3+u2L7/8Uu3atTN1KAAIF3W1FbwbBOHGr2DxwAMP6KOPPtK8efO0f/9+rV69Wjk5OcrKygrWfADgWL60FaxBEG78ChZ9+vTR2rVr9eKLL6pLly564okntHDhQk40AoBq1NVWSKxBEH78OnlTkkaOHKmRI0cGYxYACBu+tBWsQRCO+FkhABAEvrQVrEEQjggWAGAyX9oKiTUIwhPBAgBM5ktbwRoE4YpgAQAm8rWtYA2CcEWwAAAT+dJWSKxBEL4IFgBgEl/bCtYgCGcECwAwia9tBWsQhDOCBQCYwNe2QmINgvBGsAAAE/jaVrAGQbgjWABAPfnTVrAGQbgjWABAPfnaVkisQRD+CBYAUA/+tBWsQRAJCBYAUA/+tBWsQRAJCBYAECB/2gqJNQgiA8ECAALkT1vBGgSRgmABAAHwt61gDYJIQbAAgAD401ZIrEEQOQgWAOAnf9sK1iCIJAQLAPCTv20FaxBEEoIFAPjB37ZCYg2CyEKwAAA/+NtWsAZBpCFYAICPAmkrWIMg0hAsAMBH/rYVEmsQRB6CBQD4IJC2gjUIIhHBAgB8EEhbwRoEkYhgAQB1CKStkFiDIDIRLACgDoG0FaxBEKkIFgBQi0DbCtYgiFQECwCoRSBthcQaBJGLYAEANQi0rWANgkhGsACAGgTaVrAGQSQjWABANQJtKyTWIIhsBAsAqEagbQVrEEQ6ggUAXKA+bQVrEEQ6ggUAXCDQtkJiDQIQLADgPPVpK1iDAAQLAPBSn7aCNQjgZ7CYM2eOXC6X1+XKK68M1mwAEFL1aSsk1iCAJDXw9w5XXXWV3n333Z8foIHfDwEAtlSftoI1CFDJ71TQoEEDtWrVyufjy8rKVFZW5rleUlLi71MCQNDVt61gDQJU8vsci3379qlNmza67LLLlJGRocOHD9d6fHZ2thISEjyXlJSUgIcFgGCpT1shsQYBznEZhmH4evD69etVWlqqTp066dixY5o7d66OHj2qvXv3Ki4urtr7VNdYpKSkqLi4mD98AGyhoKBAqampKi8vV15eXkBrkLS0NOXn52vlypXKyMgIzqCAhUpKSpSQkFDn92+/ViHDhw/3/O+uXbuqb9++ateunV566SVNnDix2vvExMQoJibGn6cBgJCqb1vBGgT4Wb3ebnrxxRfriiuu0P79+82aBwBCqr7nVkisQYDz1StYlJaW6quvvlLr1q3NmgcAQqq+bQXvBgG8+RUsHnroIW3ZskUHDx7U//3f/+nmm29WdHS07rjjjmDNBwBBY0ZbwRoE8ObXORZHjhzRHXfcoe+++05JSUn6xS9+oY8++khJSUnBmg8Agqa+bYXEGgS4kF/BIjc3N1hzAEBImdFWsAYBquJnhQCISGa0FaxBgKoIFgAijhlthcQaBKgOwQJAxDGjrWANAlSPYAEgopjVVrAGAapHsAAQUcxoKyTWIEBNCBYAIoZZbQVrEKBmBAsAEcOstoI1CFAzggWAiGBWWyGxBgFqQ7AAEBHMaitYgwC1I1gACHtmthWsQYDaESwAhD2z2gqJNQhQF4IFgLBmZlvBGgSoG8ECQFgzs61gDQLUjWABIGyZ2VZIrEEAXxAsAIQtM9sK1iCAbwgWAMKS2W0FaxDANwQLAGHJzLZCYg0C+IpgASDsmN1WsAYBfEewABB2zG4rWIMAviNYAAgrZrcVEmsQwB8ECwBhxey2gjUI4B+CBYCwEYy2gjUI4B+CBYCwYXZbIbEGAfxFsAAQFoLRVrAGAfxHsAAQFoLRVrAGAfxHsADgeMFoKyTWIEAgCBYAHC8YbQVrECAwBAsAjhastoI1CBAYggUARwtGWyGxBgECRbAA4FjBaitYgwCBI1gAcKxgtRWsQYDAESwAOFKw2gqJNQhQHwQLAI4UrLaCNQhQPwQLAI4TzLaCNQhQPwQLAI4TrLZCYg0C1BfBAoCjBLOtYA0C1B/BAoCjBLOtYA0C1F+9gsX8+fPlcrk0ffp0k8YBgJoFs62QWIMAZgg4WGzfvl1LlixR165dzZwHAGoUzLaCNQhgjoCCRWlpqTIyMrR06VI1a9as1mPLyspUUlLidQEAfwW7rWANApgjoGCRlZWlG2+8UYMHD67z2OzsbCUkJHguKSkpgTwlgAgXzLZCYg0CmMXvYJGbm6uPP/5Y2dnZPh0/a9YsFRcXey4FBQV+DwkgsgW7rWANApingT8HFxQUaNq0adq4caNiY2N9uk9MTIxiYmICGg4ApOC3FaxBAPP4FSx27typEydOqGfPnp7bKioq9P7772vRokUqKytTdHS06UMCiFzBbisk1iCAmfwKFtdff7327Nnjddv48eN15ZVX6uGHHyZUADBdsNsK1iCAufwKFnFxcerSpYvXbU2bNlViYmKV2wGgvkLRVrAGAczFJ28CsK1gtxUSaxDAbH41FtXZvHmzCWMAgLdQtBWsQQDz0VgAsKVQtBWsQQDzESwA2E4o2gqJNQgQDAQLALYTiraCNQgQHAQLALYSqraCNQgQHAQLALYSirZCYg0CBAvBAoBthKqtYA0CBA/BAoBthKqtYA0CBA/BAoAthKqtkFiDAMFEsABgC6FqK1iDAMFFsABguVC2FaxBgOAiWACwXKjaCok1CBBsBAsAlgplW8EaBAg+ggUAS4WyrWANAgQfwQKAZULZVkisQYBQIFgAsEwo2wrWIEBoECwAWCLUbQVrECA0CBYALBHKtkJiDQKECsECQMiFuq1gDQKEDsECQMiFuq1gDQKEDsECQEiFuq2QWIMAoUSwABBSoW4rWIMAoUWwABAyVrQVrEGA0CJYAAiZULcVEmsQINQIFgBCwoq2gjUIEHoECwAhYUVbwRoECD2CBYCgs6KtkFiDAFYgWAAIOivaCtYggDUIFgCCyqq2gjUIYA2CBYCgsqKtkFiDAFYhWAAIGqvaCtYggHUIFgCCxqq2gjUIYB2CBYCgsKqtkFiDAFYiWAAICqvaCtYggLUIFgBMZ2VbwRoEsBbBAoDprGorJNYggNUIFgBMZWVbwRoEsB7BAoCprGwrWIMA1vMrWCxevFhdu3ZVfHy84uPj1a9fP61fvz5YswFwGCvbCok1CGAHfgWL5ORkzZ8/Xzt37tSOHTs0aNAg/fKXv9Snn34arPkAOIiVbQVrEMAeXIZhGPV5gObNm+sPf/iDJk6cWO3Xy8rKVFZW5rleUlKilJQUFRcX8y8KIIwUFBQoNTVV5eXlysvLC3mw2L17t7p166aYmBidOHGCv18Ak5WUlCghIaHO798Bn2NRUVGh3NxcnT59Wv369avxuOzsbCUkJHguKSkpgT4lABuzsq2QWIMAduF3Y7Fnzx7169dPZ86c0UUXXaTVq1drxIgRNR5PYwGEP6vbCsMwlJaWpvz8fK1cuVIZGRkhfX4gEvjaWDTw94E7deqkXbt2qbi4WK+88ooyMzO1ZcsWde7cudrjY2JiFBMT4+/TAHAQq9sK3g0C2IffwaJRo0ZKTU2VJPXq1Uvbt2/XU089pSVLlpg+HAD7s/qdIBJrEMBO6v05Fm6322vVASCyWN1W8G4QwF78aixmzZql4cOHq23btvrhhx+0evVqbd68WRs2bAjWfABszA5tBWsQwF78ChYnTpzQ3XffrWPHjikhIUFdu3bVhg0bdMMNNwRrPgA2ZnVbIbEGAezGr2CxfPnyYM0BwGHs0FawBgHsh58VAiAgdmgrWIMA9kOwAOA3O7QVEmsQwI4IFgD8Zoe2gjUIYE8ECwB+sUtbwRoEsCeCBQC/2KGtkFiDAHZFsADgM7u0FaxBAPsiWADwmV3aCtYggH0RLAD4xC5thcQaBLAzggUAn9ilrWANAtgbwQJAnezUVrAGAeyNYAGgTnZpKyTWIIDdESwA1MpObQVrEMD+CBYAamWntoI1CGB/BAsANbJTWyGxBgGcgGABoEZ2aitYgwDOQLAAUC27tRWsQQBnIFgAqJad2gqJNQjgFAQLAFXYra1gDQI4B8ECQBV2aytYgwDOQbAA4MVubYXEGgRwEoIFAC92aytYgwDOQrAA4GHHtoI1COAsBAsAHnZrKyTWIIDTECwASLJnW8EaBHAeggUASfZsK1iDAM5DsABgy7ZCYg0COBHBAoAt2wrWIIAzESyACGfXtoI1COBMBAsgwtmxrZBYgwBORbAAIphd2wrWIIBzESyACGbXtoI1COBcBAsgQtm1rZBYgwBORrAAIpRd2wrWIICzESyACGTntoI1COBsBAsgAtm1rZBYgwBOR7AAIoyd2wrWIIDzESyACGPntoI1COB8fgWL7Oxs9enTR3FxcWrRooVGjx6t/Pz8YM0G+O/IESkvr/JXVGHntkJiDQKEA7+CxZYtW5SVlaWPPvpIGzdu1NmzZzVkyBCdPn06WPMBvlu+XGrXTho0qPLX5cutnsh27NxWsAYBwoPLMAwj0DsXFRWpRYsW2rJli6677rpqjykrK1NZWZnneklJiVJSUlRcXMy/SGCeI0dktGsnl9v9823R0dLBg1JysmVj2UlBQYFSU1NVXl6uvLw82wWL3bt3q1u3boqJidGJEyf4+wGwmZKSEiUkJNT5/bte51gUFxdLkpo3b17jMdnZ2UpISPBcUlJS6vOUQPX27fMOFZJUUSHt32/NPDZk57ZCYg0ChIuAGwu3261Ro0bp1KlT+utf/1rjcTQWCIkjR+Ru21ZR5/12NqKi5Dp0iMZC9m8rDMNQWlqa8vPztXLlSmVkZFg9EoALBL2xyMrK0t69e5Wbm1vrcTExMYqPj/e6AKZLTta7Y8boH/+8+g9JDzRpoj0nT1o5lW3Yva3g3SBA+AgoWEyZMkVvvvmm8vLylMy/BmETe/v2VXtJM/v21S+7dtVTpaUaNGiQ9uzZY/VolrL7O0Ek1iBAOPErWBiGoSlTpmjt2rV677331KFDh2DNBQTkqKQjqalauXmzevfurW+//Tbiw4Xd2wreDQKEF7+CRVZWllauXKnVq1crLi5OhYWFKiws1E8//RSs+YCANGvWTO+8807EhwsntBWsQYDw4lewWLx4sYqLi5Wenq7WrVt7LmvWrAnWfEDACBf2bysk1iBAuPF7FVLdZdy4cUEaD6ifSA4XTmgrWIMA4YefFYKwF6nhwgltBWsQIPwQLBARIi1cOKGtkFiDAOGIYIGIEUnhwgltBWsQIDwRLBBRIiFcOKWtYA0ChCeCBSJOuIcLJ7QVEmsQIFwRLBCRwjVcOKWtYA0ChC+CBSJWOIYLp7QVrEGA8EWwQEQLp3DhlLZCYg0ChDOCBSJeuIQLp7QVrEGA8EawAOT8cOGktoI1CBDeCBbAPzk5XDilrZBYgwDhjmABnMeJ4cJJbQVrECD8ESyACzgtXDiprWANAoQ/ggVQDaeECye1FRJrECASECyAGjghXDiprWANAkQGggVQCzuHC6e1FaxBgMhAsADqYNdw4aS2QmINAkQKggXgA7uFC6e1FaxBgMhBsAB8ZKdw4bS2gjUIEDkIFoAf7BAunNZWSKxBgEhCsAD8ZHW4cFpbwRoEiCwECyAAVoULJ7YVrEGAyEKwAAJkRbhwWlshsQYBIg3BAqiHUIYLJ7YVrEGAyEOwAOopVOHCiW0FaxAg8hAsABMEO1w4sa2QWIMAkYhgAZgkmOHCiW0FaxAgMhEsABMFI1w4ta1gDQJEJoIFYDKzw4UT2wqJNQgQqQgWQBCYFS6c2lawBgEiF8ECCBIzwoVT2wrWIEDkIlgAQVSfcOHUtkJiDQJEMoIFEGSBhgunthWsQYDIRrAAQsDfcOHktoI1CBDZCBZAiPgTLpzaVkisQYBIR7AAQsiXcOHktoI1CACCBRBidYULJ7cVrEEA+B0s3n//fd10001q06aNXC6XXnvttSCMBYS3msLFN9u2aV9Oji6V89oKSdqwfLnSJWUMGMAaBIhQfgeL06dPq1u3bnr22WeDMQ8QMS4MF8uvvVat+vbVO//4hw5JSv/qK6tH9IuxbJlmPP208iQt27hRWr7c6pEAWKCBv3cYPny4hg8f7vPxZWVlKisr81wvKSnx9ymBsHUuXIxNT9eC3bs9ST9aku67Txo6VEpOtnBCHx05It13X+XcklyG4az5AZgm6OdYZGdnKyEhwXNJSUkJ9lMCjtKsWTPlPvGE55uyR0WFtH+/FSP5JT8/X/8+bpxcbrf3FxwyPwBzBT1YzJo1S8XFxZ5LQUFBsJ8ScJy4nj1lRF3wxzE6WkpNtWYgH+Tn52vs2LHq3LmzFm/apIoLD7D5/ACCI+jBIiYmRvHx8V4XABdITpYrJ6fym7FU+euSJbZcI5wfKFatWiW3261eo0bpyKOPOmJ+AMHl9zkWAIJk4sTKcxL276/8l77Nvinn5+friSee0Isvvij3P9ceo0aN0uzZs9WzZ8/KgyZNsu38AEKDYAHYSXKy7b4h+xQozrHh/ABCy+9gUVpaqv3nnZB14MAB7dq1S82bN1fbtm1NHQ6AdfwKFADwT34Hix07dmjgwIGe6zNmzJAkZWZm6s9//rNpgwGwBoECQH34HSzS09NlGEYwZgFgIQIFADNwjgUQ4QgUAMxEsAAiFIECQDAQLIAIQ6AAEEwECyBCECgAhALBAghzBAoAoUSwAMIUgQKAFQgWQJghUACwEsECCBMECgB2QLAAHI5AAcBOCBaAQxEoANgRwQJwGAIFADsjWAAOQaAA4AQEC8DmCBQAnIRgAdgUgQKAExEsAJshUABwMoIFYBMECgDhgGABWIxAASCcECwAixAoAIQjggUQYgQKAOGMYAGECIECQCQgWABBRqAAEEkIFkCQECgARCKCBWAyAgWASEawAExCoAAAggVQbwQKAPgZwQIIEIECAKoiWAB+IlAAQM0IFoCPCBQAUDeCBVAHAgUA+I5gAdSAQAEA/iNYABcgUABA4AgWwD8RKACg/ggWiHgECgAwD8ECEYtAAQDmI1gg4hAoACB4CBaIGAQKAAg+ggXCHoECAEInKpA7Pfvss2rfvr1iY2PVt29fbdu2zey5gIBcKimtsFA6ckT5+fkaO3asOnfurFWrVsntdmvUqFHauXOn/vKXvxAqACAI/G4s1qxZoxkzZuj5559X3759tXDhQg0dOlT5+flq0aJFMGYEfNLlb3/TIUnRmzbJnZKiP7pcWmUYkmgoACBUXIbxz795fdS3b1/16dNHixYtkiS53W6lpKRo6tSpmjlzZpXjy8rKVFZW5rleUlKilJQUFRcXKz4+vp7jA/905Ijcbdsq6rzfzv+QNOmGGzRl/nwCBQDUU0lJiRISEur8/u3XKqS8vFw7d+7U4MGDf36AqCgNHjxYH374YbX3yc7OVkJCgueSkpLiz1MCvtm3zytUSJV13J8eeYRQAQAh5Few+Pbbb1VRUaGWLVt63d6yZUsVFhZWe59Zs2apuLjYcykoKAh8WqAmHTvKcLm8b4uOllJTrZkHACJUQCdv+iMmJkbx8fFeF8B0yclyLV1aGSakyl+XLJGSk62dCwAijF8nb15yySWKjo7W8ePHvW4/fvy4WrVqZepggN8mTpSGDpX2769sKggVABByfjUWjRo1Uq9evbRp0ybPbW63W5s2bVK/fv1MHw7wW3KylJ5OqAAAi/j9dtMZM2YoMzNTvXv31jXXXKOFCxfq9OnTGj9+fDDmAwAADuJ3sLjttttUVFSkxx57TIWFherevbvefvvtKid0AgCAyOP351jUl6/vgwUAAPYRlM+xAAAAqA3BAgAAmIZgAQAATEOwAAAApiFYAAAA0xAsAACAaQgWAADANAQLAABgGr8/ebO+zn0eV0lJSaifGgAABOjc9+26Plcz5MHihx9+kCSlpKSE+qkBAEA9/fDDD0pISKjx6yH/SG+3261vvvlGcXFxcrlcoXzqkCgpKVFKSooKCgr4yHIL8Ppbi9ffWrz+1gr3198wDP3www9q06aNoqJqPpMi5I1FVFSUkiPgR1rHx8eH5W8sp+D1txavv7V4/a0Vzq9/bU3FOZy8CQAATEOwAAAApiFYmCwmJkazZ89WTEyM1aNEJF5/a/H6W4vX31q8/pVCfvImAAAIXzQWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AIkoMHD2rixInq0KGDGjdurMsvv1yzZ89WeXm51aOFrWeffVbt27dXbGys+vbtq23btlk9UkTIzs5Wnz59FBcXpxYtWmj06NHKz8+3eqyINX/+fLlcLk2fPt3qUSLG0aNHNXbsWCUmJqpx48a6+uqrtWPHDqvHsgzBIki++OILud1uLVmyRJ9++qmefPJJPf/883rkkUesHi0srVmzRjNmzNDs2bP18ccfq1u3bho6dKhOnDhh9Whhb8uWLcrKytJHH32kjRs36uzZsxoyZIhOnz5t9WgRZ/v27VqyZIm6du1q9SgR4+TJk+rfv78aNmyo9evX67PPPtOCBQvUrFkzq0ezDJ9jEUJ/+MMftHjxYn399ddWjxJ2+vbtqz59+mjRokWSKn/YXUpKiqZOnaqZM2daPF1kKSoqUosWLbRlyxZdd911Vo8TMUpLS9WzZ08999xz+v3vf6/u3btr4cKFVo8V9mbOnKmtW7fqgw8+sHoU26CxCKHi4mI1b97c6jHCTnl5uXbu3KnBgwd7bouKitLgwYP14YcfWjhZZCouLpYkfq+HWFZWlm688UavPwcIvtdff129e/fWmDFj1KJFC/Xo0UNLly61eixLESxCZP/+/XrmmWd03333WT1K2Pn2229VUVGhli1bet3esmVLFRYWWjRVZHK73Zo+fbr69++vLl26WD1OxMjNzdXHH3+s7Oxsq0eJOF9//bUWL16sjh07asOGDbr//vv1r//6r3rhhResHs0yBAs/zZw5Uy6Xq9bLF1984XWfo0ePatiwYRozZozuvfdeiyYHgi8rK0t79+5Vbm6u1aNEjIKCAk2bNk2rVq1SbGys1eNEHLfbrZ49e2revHnq0aOHJk2apHvvvVfPP/+81aNZpoHVAzjNgw8+qHHjxtV6zGWXXeb53998840GDhyoa6+9Vjk5OUGeLjJdcsklio6O1vHjx71uP378uFq1amXRVJFnypQpevPNN/X+++8rOTnZ6nEixs6dO3XixAn17NnTc1tFRYXef/99LVq0SGVlZYqOjrZwwvDWunVrde7c2eu2tLQ0vfrqqxZNZD2ChZ+SkpKUlJTk07FHjx7VwIED1atXL61YsUJRURREwdCoUSP16tVLmzZt0ujRoyVV/iti06ZNmjJlirXDRQDDMDR16lStXbtWmzdvVocOHaweKaJcf/312rNnj9dt48eP15VXXqmHH36YUBFk/fv3r/L26i+//FLt2rWzaCLrESyC5OjRo0pPT1e7du30xz/+UUVFRZ6v8a9o882YMUOZmZnq3bu3rrnmGi1cuFCnT5/W+PHjrR4t7GVlZWn16tX6y1/+ori4OM95LQkJCWrcuLHF04W/uLi4KuezNG3aVImJiZznEgIPPPCArr32Ws2bN0+33nqrtm3bppycnIhuqAkWQbJx40bt379f+/fvr1IL8w5f8912220qKirSY489psLCQnXv3l1vv/12lRM6Yb7FixdLktLT071uX7FiRZ1rQ8Dp+vTpo7Vr12rWrFl6/PHH1aFDBy1cuFAZGRlWj2YZPscCAACYhqU/AAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAEzz/ylSMVog/HVQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make your own set of vertices - anything you would like!\n",
    "boundary = np.array([(0, 0), (2, 1), (4, 7), (1, 1), (0, 2)])\n",
    "\n",
    "# Then see what types of perimeters they generate\n",
    "for boundary_type in ['convex_hull','square','rectangle','polygon']:\n",
    "    plot_boundary(boundary_type, XYBoundaryConstraint(boundary, boundary_type))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spacing constraints\n",
    "\n",
    "The next most common constraint in a wind farm design optimization problem is on the allowable inter-turbine spacing in the farm.  Instinctively, turbines will try to spread out within the wind farm to minimize wake losses, but a minimum constraint can also help to ensure that turbines not get placed too close together.\n",
    "\n",
    "The following provides a simple example of implementation of a minimum spacing constraint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up dummy design variables and cost model component. \n",
    "# This example includes 2 turbines (n_wt=2) located at x,y=0.5,0.5 and 1.5,1.5 respectively\n",
    "\n",
    "x = [0.5,1.5]\n",
    "y = [.5,1.5]\n",
    "dummy_cost = CostModelComponent(input_keys=[],\n",
    "                                n_wt=2,\n",
    "                               cost_function=lambda : 1)   \n",
    "\n",
    "# a function to plot a spacing constraint for a Topfarm problem\n",
    "def plot_spacing(name, constraint_comp):\n",
    "    tf = TopFarmProblem(\n",
    "        design_vars={'x':x, 'y':y}, # setting up the turbine positions as design variables\n",
    "        cost_comp=dummy_cost, # using dummy cost model\n",
    "        constraints=[constraint_comp], # constraint set up for the boundary type provided\n",
    "        plot_comp=XYPlotComp()) # support plotting function\n",
    "    tf.evaluate()\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(name)\n",
    "    tf.plot_comp.plot_constraints() # plot constraints is a helper function in topfarm to plot constraints\n",
    "    plt.plot(x,y,'.b', label='Wind turbines') # plot the turbine locations\n",
    "    plt.axis('equal')\n",
    "    plt.legend() # add the legend\n",
    "    plt.ylim([0,3])    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To employ the spacing constraint, you must specify the minimum distance between turbines in meters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_spacing('spacing', SpacingConstraint(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Play around with the spacing constraint size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n",
      "INFO: checking out_of_order\n",
      "INFO: checking system\n",
      "INFO: checking solvers\n",
      "INFO: checking dup_inputs\n",
      "INFO: checking missing_recorders\n",
      "INFO: checking unserializable_options\n",
      "INFO: checking comp_has_no_outputs\n",
      "INFO: checking auto_ivc_warnings\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
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