{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Geometrie" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n" ] }, { "cell_type": "code", "execution_count": 1, "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": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([11, 81, 47, 36, 28, 80, 76, 17], dtype=int32)" ] }, "execution_count": 19, "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": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "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": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import sympy as sy\n", "from sympy.geometry import Point, Segment, Circle, Line, Triangle" ] }, { "cell_type": "code", "execution_count": 24, "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": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Point.is_collinear(x, y, z)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Point.is_collinear(x, y, zp)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "seg1 = Segment(x, z)\n", "seg2 = Segment(y, zp)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[Point(1, 1)]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "seg1.intersection(seg2)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Point(1, 1)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "seg1.midpoint" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "c = Circle(x, 5)\n", "l = Line(Point(5, -5), Point(5, 5)) " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.is_tangent(l)" ] }, { "cell_type": "code", "execution_count": 50, "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": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l2 = Line(Point(2, -4), Point(3, -2))\n", "c.intersection(l2)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ " " ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }