uetchy/bezier_curve.ipynb

## bezier_curve.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "import numpy as np\n",
    "from functools import reduce\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Bezier:\n",
    "\n",
    "    def __init__(self, ndim, points):\n",
    "        self.ndim = ndim\n",
    "        self.points = np.array(points)\n",
    "\n",
    "    def combination(self, n, r):\n",
    "        return factorial(n) / factorial(r)\n",
    "\n",
    "    def bernstein(self, n, i, t):\n",
    "        '''\n",
    "        B_i^n = \\binom ni (1-t)^{n-i} t^i\n",
    "        '''\n",
    "        return self.combination(n, i) * (1 - t)**(n - i) * t**i\n",
    "\n",
    "    def R(self, n, t, p):\n",
    "        '''\n",
    "        R(T) = \\sum^n_{i=0} B_i^n(t) P_i\n",
    "        '''\n",
    "        return reduce(lambda s, i: s + self.bernstein(n, i, t) * p[i],\n",
    "                      range(n + 1))\n",
    "\n",
    "    def render(self, t):\n",
    "        xr = self.R(self.ndim, t, self.points.T[0])\n",
    "        yr = self.R(self.ndim, t, self.points.T[1])\n",
    "        return (xr, yr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bezier_points = np.array([(0, 0), (1, 3), (5, 3), (6, 0)])\n",
    "renderer = Bezier(3, bezier_points)\n",
    "rpoints = np.array([renderer.render(tn * 0.01) for tn in range(100)])\n",
    "rpoints = np.append(rpoints, [bezier_points[-1]], axis=0)\n",
    "plt.plot(rpoints.T[0], rpoints.T[1], 'b')\n",
    "plt.plot(bezier_points.T[0], bezier_points.T[1], 'o')\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
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [],
	"source": [
	"from math import factorial\n",
	"import numpy as np\n",
	"from functools import reduce\n",
	"import matplotlib.pyplot as plt\n",
	"%matplotlib inline"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [],
	"source": [
	"class Bezier:\n",
	"\n",
	" def __init__(self, ndim, points):\n",
	" self.ndim = ndim\n",
	" self.points = np.array(points)\n",
	"\n",
	" def combination(self, n, r):\n",
	" return factorial(n) / factorial(r)\n",
	"\n",
	" def bernstein(self, n, i, t):\n",
	" '''\n",
	" B_i^n = \\binom ni (1-t)^{n-i} t^i\n",
	" '''\n",
	" return self.combination(n, i) * (1 - t)*(n - i) t**i\n",
	"\n",
	" def R(self, n, t, p):\n",
	" '''\n",
	" R(T) = \\sum^n_{i=0} B_i^n(t) P_i\n",
	" '''\n",
	" return reduce(lambda s, i: s + self.bernstein(n, i, t) * p[i],\n",
	" range(n + 1))\n",
	"\n",
	" def render(self, t):\n",
	" xr = self.R(self.ndim, t, self.points.T[0])\n",
	" yr = self.R(self.ndim, t, self.points.T[1])\n",
	" return (xr, yr)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 8,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"bezier_points = np.array([(0, 0), (1, 3), (5, 3), (6, 0)])\n",
	"renderer = Bezier(3, bezier_points)\n",
	"rpoints = np.array([renderer.render(tn * 0.01) for tn in range(100)])\n",
	"rpoints = np.append(rpoints, [bezier_points[-1]], axis=0)\n",
	"plt.plot(rpoints.T[0], rpoints.T[1], 'b')\n",
	"plt.plot(bezier_points.T[0], bezier_points.T[1], 'o')\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
	}