2D_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import math "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Takes lines in the form of ax + by = c\n",
    "class Line:\n",
    "    def __init__(self, a, b, c):\n",
    "        self.formula = {'a': a, 'b':b, 'c':c}\n",
    "        self.s_formula = self.parse_to_s(a, b, c)\n",
    "        \n",
    "        \n",
    "    def parse_to_s(self, a, b, c):\n",
    "        if b == 0:\n",
    "            vertical = True\n",
    "            m = None\n",
    "            n = c/a\n",
    "        else:\n",
    "            vertical = False\n",
    "            m = -a/b\n",
    "            n = c/b\n",
    "        return {'m':m, 'n':n, 'vertical':vertical}\n",
    "    \n",
    "#     def plug(self, x):\n",
    "#         if self.s_formula['vertical'] == False:\n",
    "            \n",
    "        \n",
    "    def plot(self, ax=False, axis=[-10, 10, -10, 10], *args, **kwargs):\n",
    "        if self.s_formula['vertical'] == False:\n",
    "            x = np.linspace(axis[0], axis[1], 10)\n",
    "            m, b = self.s_formula['m'], self.s_formula['n']\n",
    "            y = [m*i + b for i in x]\n",
    "        \n",
    "        else:\n",
    "            x = [self.s_formula['n']] * 10\n",
    "            y = np.linspace(axis[2], axis[3], 10)\n",
    "            \n",
    "        if not ax:\n",
    "            ax = default_axes(*args, **kwargs)\n",
    "            \n",
    "        ax.plot(x, y, *args, **kwargs)\n",
    "        return ax\n",
    "    \n",
    "    \n",
    "    def has(self, point):\n",
    "        a, b, c = self.formula['a'], self.formula['b'], self.formula['c']\n",
    "        x = point[0]\n",
    "        y = point[1]\n",
    "        return a*x + b*y == c\n",
    "    \n",
    "    \n",
    "    def distance(self, point):\n",
    "        a, b, c = self.formula['a'], self.formula['b'], self.formula['c']\n",
    "        x, y = point\n",
    "        numerator = abs(a*x + b*y - c)\n",
    "        denominator = norm([a, b])\n",
    "        return numerator/denominator\n",
    "    \n",
    "    \n",
    "    def get_perpendicular(self, point):\n",
    "        a, b, c = self.formula['a'], self.formula['b'], self.formula['c']\n",
    "        a1 = -1 * b\n",
    "        b1 = a\n",
    "        c1 = point[0] * a1 + point[1] * b1\n",
    "        return Line(a1, b1, c1)\n",
    "    \n",
    "    \n",
    "    def get_perp_intersection(self, point):\n",
    "        a, b, c = self.formula['a'], self.formula['b'], self.formula['c']\n",
    "        d = self.get_perpendicular(point).formula['c']\n",
    "        y = round((a*d + b*c)/(a**2 + b**2), 6)\n",
    "        x = round((c - b*y)/a, 6)\n",
    "        return [x, y]\n",
    "    \n",
    "\n",
    "class Circle:\n",
    "    def __init__(self, c, r):\n",
    "        self.formula = {'c':c, 'r':r}\n",
    "        \n",
    "    def plot(self, ax=False, axis=[-10, 10, -10, 10], figsize=(10,10), *args, **kwargs):\n",
    "        c, r = self.formula['c'], self.formula['r']\n",
    "        C = plt.Circle(c, r, fill=False, *args, **kwargs)\n",
    "        if not ax:\n",
    "            ax = default_axes(*args, **kwargs)\n",
    "        ax.add_artist(C)\n",
    "        return ax\n",
    "    \n",
    "    \n",
    "    def has(self, point):\n",
    "        c, r = self.formula['c'], self.formula['r']\n",
    "        return distance(c, point) == r\n",
    "    \n",
    "    \n",
    "    def invert_point(self, point):\n",
    "        c, r = self.formula['c'], self.formula['r']\n",
    "        theta = math.atan((point[1] - c[1])/(point[0] - c[0]))\n",
    "        inv_r = r/distance(point, c)\n",
    "        x0 = round(inv_r * math.cos(theta), 6)\n",
    "        y0 = round(inv_r * math.sin(theta), 6)\n",
    "        return [x0, y0]\n",
    "    \n",
    "    \n",
    "    def invert(self, shape):\n",
    "        c, r = self.formula['c'], self.formula['r']\n",
    "        if isinstance(shape, Line):\n",
    "            if shape.has(c):\n",
    "                return Line(shape.formula['a'], shape.formula['b'], shape.formula['c'])\n",
    "            elif shape.distance(c) == r:\n",
    "                return Circle(c, r)\n",
    "            else:\n",
    "                P = c\n",
    "                perp_point = shape.get_perp_intersection(c)\n",
    "                R = self.invert_point(perp_point)\n",
    "                Q = midpoint(P, R)\n",
    "                print(P, Q, R)\n",
    "                return Circle(Q, distance(P, Q))\n",
    "        \n",
    "        elif isinstance(shape, Circle):\n",
    "            c2, r2 = shape.formula['c'], shape.formula['r']\n",
    "            if c2 == c and r2 == r:\n",
    "                return Circle(c, r)\n",
    "#             elif c2 = c:\n",
    "                \n",
    "#                 return Circle(c, )\n",
    "#             elif:\n",
    "            \n",
    "#         else:\n",
    "#             return None\n",
    "\n",
    "\n",
    "def default_axes(figsize = (10,10), axis=[-10, 10, -10, 10], coords=True, *args, **kwargs):\n",
    "    f, axes = plt.subplots(figsize=figsize, *args, **kwargs)\n",
    "    plt.axis(axis)\n",
    "    if coords:\n",
    "        plt.axhline(0, color='k')\n",
    "        plt.axvline(0, color='k')\n",
    "    return axes\n",
    "\n",
    "\n",
    "def distance(point1, point2):\n",
    "    return math.sqrt((point1[0] - point2[0])**2 + (point1[1] - point2[1])**2)\n",
    "\n",
    "\n",
    "def norm(vector):\n",
    "    return math.sqrt(vector[0]**2 + vector[1]**2)\n",
    "\n",
    "\n",
    "def midpoint(point1, point2):\n",
    "    return [(point1[0] + point2[0])/2, (point1[1] + point2[1])/2]\n",
    "\n",
    "\n",
    "def points2l(point1, point2):\n",
    "    a = point1[1] - point2[1]\n",
    "    b = -1 * (point1[0] - point2[0])\n",
    "    c = a*point1[0] + b*point1[1]\n",
    "    return Line(a, b, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "origin = [0, 0]\n",
    "vi = [1, 0]\n",
    "vj = [0, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f88d1046350>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tl = Line(1, -2, 0)\n",
    "tl2 = tl.get_perpendicular(origin)\n",
    "\n",
    "base = default_axes()\n",
    "tl.plot(ax=base, color='g')\n",
    "tl2.plot(ax=base)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = Circle([0,0], 1)\n",
    "# l = Line(-1, 2, 0)\n",
    "l = points2l([0, 5], [-2, 3])\n",
    "l2 = Line(1, 1, -5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0] [0.1, -0.1] [0.2, -0.2]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f88f0923450>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = default_axes()\n",
    "b.plot(ax)\n",
    "l.plot(ax)\n",
    "nc = b.invert(l)\n",
    "nc.plot(ax, color='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.6 64-bit ('base': conda)",
   "language": "python",
   "name": "python37664bitbaseconda9e65c572ed0444d5bc39393b7e6857ff"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}