{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Geometrie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Konvexe Hülle\n",
    "\n",
    "SciPy's [spatial Modul](http://docs.scipy.org/doc/scipy-dev/reference/spatial.html)\n",
    "beinhaltet zum Beispiel eine Methode um die [konvexe Hülle](http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.spatial.ConvexHull.html) von Punkten finden zu können.\n",
    "Es ist ein front-end für [QHull](http://www.qhull.org/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 21, 60, 73, 39, 96,  0, 44, 19], dtype=int32)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.spatial import ConvexHull\n",
    "\n",
    "pts = np.random.normal(size=(100,2))\n",
    "chull = ConvexHull(pts)\n",
    "chull.vertices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0fdf7dde50>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0ZE6lnqJciXKW1HFpCNpxaJadRs5cqiBrupwP/cOHjwDpVKlS1e3hr28seTuU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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fdef95810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "for simplex in chull.simplices:\n",
    "    plt.plot(pts[simplex, 0], pts[simplex, 1], \"g-\", lw=2, zorder=1)\n",
    "plt.scatter(pts[:,0], pts[:,1], zorder=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sympy Geometry Module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting permissions of DOT_SAGE directory so only you can read and write it.\n"
     ]
    }
   ],
   "source": [
    "import sympy as sy\n",
    "from sympy.geometry import Point, Segment, Circle, Line, Triangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = Point(0, 0)\n",
    "y = Point(1, 1)\n",
    "z = Point(2, 2)\n",
    "zp = Point(1, 0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Point.is_collinear(x, y, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Point.is_collinear(x, y, zp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "seg1 = Segment(x, z)\n",
    "seg2 = Segment(y, zp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Point(1, 1)]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seg1.intersection(seg2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Point(1, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seg1.midpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c = Circle(x, 5)\n",
    "l = Line(Point(5, -5), Point(5, 5)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.is_tangent(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Point(-sqrt(61)/5 + 16/5, -2*sqrt(61)/5 - 8/5),\n",
       " Point(sqrt(61)/5 + 16/5, -8/5 + 2*sqrt(61)/5)]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l2 = Line(Point(2, -4), Point(3, -2))\n",
    "c.intersection(l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    " "
   ]
  }
 ],
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