{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Minimum Enclosing Circle\n", "\n", "Try to find the minimum enclosing circle using scipy.optimize.minimize, using the nelder-mead algorithm" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sqrt\n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt\n", "\n", "x = [1.0, 3.0, 2.5, 4.0, 5.0, 6.0, 5.0]\n", "y = [3.0, 1.0, 3.0, 6.0, 7.0, 7.0, 2.0]\n", "\n", "def dist(p, q):\n", " return sqrt((p[0]-q[0])**2 + (p[1]-q[1])**2)\n", "def max_distance(c):\n", " return max([dist(p, c) for p in zip(x, y)])\n", "\n", "c = minimize(max_distance, [0.0, 0.0], method=\"nelder-mead\").x\n", "ax = plt.gca()\n", "ax.set_xlim((0, 8))\n", "ax.set_ylim((0, 8))\n", "ax.set_aspect(\"equal\")\n", "plt.plot(x, y, \"g.\")\n", "ax.add_artist(plt.Circle(c, max_distance(c), color=\"r\", fill=False))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualization of nummerical search by the nelder-mead algorithm" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sqrt\n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt\n", "\n", "x = [1.0, 3.0, 2.5, 4.0, 5.0, 6.0, 5.0]\n", "y = [3.0, 1.0, 3.0, 6.0, 7.0, 7.0, 2.0]\n", "trace = []\n", "\n", "def dist(p, q):\n", " return sqrt((p[0]-q[0])**2 + (p[1]-q[1])**2)\n", "def max_distance(c):\n", " trace.append(c)\n", " return max([dist(p, c) for p in zip(x, y)])\n", "\n", "c = minimize(max_distance, [0.0, 0.0], \n", " method=\"nelder-mead\").x\n", "ax = plt.gca()\n", "ax.set_xlim((0, 8))\n", "ax.set_ylim((0, 8))\n", "ax.set_aspect(\"equal\")\n", "plt.plot(x, y, \"g.\")\n", "plt.plot(*zip(*trace), \"b.-\")\n", "ax.add_artist(plt.Circle(c, max_distance(c), color=\"r\", fill=False))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\"Finding the minimum enclosing circle using different optimization\n", "algorithms and different functions\n", "\"\"\"\n", "\n", "from math import sqrt\n", "import math \n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "solvers = [\n", " 'nelder-mead',\n", " 'powell',\n", " 'cg',\n", " 'bfgs',\n", "# 'Newton-CG',\n", " 'L-BFGS-B',\n", " 'TNC',\n", " 'COBYLA',\n", " 'SLSQP',\n", "# 'dogleg',\n", "# 'trust-ncg',\n", "# 'trust-exact',\n", "# 'trust-krylov'\n", "]\n", "\n", "######################################################################\n", "\n", "points_X = [1.0, 3.0, 2.5, 4.0, 5.0, 6.0, 5.0]\n", "points_Y = [3.0, 1.0, 3.0, 6.0, 7.0, 7.0, 2.0]\n", "\n", "points = list(zip(points_X, points_Y))\n", "\n", "######################################################################\n", "# Minimum enclosing circle solver\n", "\n", "\n", "def distance(p, q):\n", " \"\"\" compute distance between d-dimensional points p and q \"\"\"\n", " return sqrt(sum([(i-j)**2 for i, j in zip(p, q)]))\n", "\n", "def distance_max(c):\n", " \"\"\"computes the distance to the point furthest away from c\"\"\"\n", " return max([distance(p, c) for p in points])\n", "\n", "def distance_max_square(c):\n", " \"\"\"computes the distance to the point furthest away from c\"\"\"\n", " return max([(p[0]-c[0])**2+(p[1]-c[1])**2 for p in points])\n", "\n", "def distance_smooth_max(c):\n", " \"\"\"computes the distance to the point furthest away from c\"\"\"\n", " return math.log(sum([math.exp((p[0]-c[0])**2+(p[1]-c[1])**2) for p in points]))\n", "\n", "def solve_and_plot(function, method, color, linestyle):\n", " solution = minimize(function, [0.0, 0.0], method=method)\n", " cx, cy = solution.x\n", " c = (cx, cy)\n", " r = distance_max(c)\n", "\n", " plt.plot([cx], [cy], color+\"o\") # center point\n", " circle = plt.Circle(c, r, color=color, fill=False, linestyle=linestyle)\n", " ax.add_artist(circle)\n", "\n", "plt.suptitle('Smallest enclosing circle\\n\\\n", "Function: red = max distance, \\\n", "green = max distance-squared, \\\n", "blue = \"smooth\"-max distance-squared')\n", " \n", "for idx, opt_algorithm in enumerate(solvers):\n", " plt.subplot(2, 4, idx+1)\n", " plt.title(opt_algorithm)\n", " ax = plt.gca()\n", " ax.set_xlim((-1,9))\n", " ax.set_ylim((-1,9))\n", " ax.set_aspect(\"equal\")\n", " \n", " plt.plot(points_X, points_Y, \"g.\") # data points (green dots)\n", " \n", " solve_and_plot(distance_max, opt_algorithm, 'r', \"-\")\n", " solve_and_plot(distance_max_square, opt_algorithm, 'g', \"--\")\n", " solve_and_plot(distance_smooth_max, opt_algorithm, 'b', \":\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MINIMUM ENCLOSING CIRCLE\n", " final_simplex: (array([[4.16660681, 4.16669429],\n", " [4.16670636, 4.16662781],\n", " [4.16656007, 4.16670588]]), array([3.37475212, 3.3747666 , 3.37476777]))\n", " fun: 3.3747521163598315\n", " message: 'Optimization terminated successfully.'\n", " nfev: 218\n", " nit: 114\n", " status: 0\n", " success: True\n", " x: array([4.16660681, 4.16669429])\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sqrt\n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "opt_algorithm = 'nelder-mead' # Default is BFGS (fails)\n", "\n", "######################################################################\n", "\n", "points_X = [1.0, 3.0, 2.5, 4.0, 5.0, 6.0, 5.0]\n", "points_Y = [3.0, 1.0, 3.0, 6.0, 7.0, 7.0, 2.0]\n", "\n", "points = list(zip(points_X, points_Y))\n", "\n", "######################################################################\n", "# Minimum enclosing circle solver\n", "\n", "print(\"MINIMUM ENCLOSING CIRCLE\")\n", " \n", "def distance_max(c):\n", " \"\"\"computes the distance to the point furthest away from c\"\"\"\n", " return max([distance(p, c) for p in points])\n", "\n", "solution = minimize(distance_max, [0.0, 0.0], method=opt_algorithm)\n", "\n", "cx, cy = solution.x\n", "c = (cx, cy)\n", "r = distance_max(c)\n", "\n", "print(solution)\n", "\n", "######################################################################\n", "# 3D plot for minimum enclosing circle\n", "\n", "x_min = min(points_X)\n", "x_max = max(points_X)\n", "y_min = min(points_Y)\n", "y_max = max(points_Y)\n", "z_min = distance_max((cx, cy))\n", "z_max = max([distance_max(p) for p in points])\n", "\n", "grid_x_values = np.arange(x_min, x_max, (x_max-x_min)/100.0)\n", "grid_y_values = np.arange(y_min, y_max, (y_max-y_min)/100.0)\n", "\n", "X, Y = np.meshgrid(grid_x_values, grid_y_values)\n", "\n", "Z = np.zeros(X.shape)\n", "for px, py in points:\n", " Z = np.maximum(Z, np.sqrt((X-px)**2 + (Y-py)**2))\n", "\n", "plt.subplot(1, 2, 1, projection='3d')\n", "plt.title(\"Maximum point distance\")\n", "\n", "ax = plt.gca()\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_zlabel(\"max distance\")\n", "ax.set_zlim(z_min, z_max)\n", "plt.tight_layout()\n", "\n", "surf = ax.plot_surface(X, Y, Z)\n", "ax.scatter([cx], [cy], [z_min], c=\"red\")\n", "\n", "######################################################################\n", "# Minimum enclosing circle - contour plot\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.title(\"Maximum point distance\")\n", "plt.plot(points_X, points_Y, \"or\")\n", "CS = plt.contour(X, Y, Z)\n", "plt.clabel(CS, inline=1, fontsize=10, fmt=\"%1.2f\")\n", "\n", "######################################################################\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }