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@gntlechaos
Created April 10, 2022 02:39
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{
"cells": [
{
"cell_type": "raw",
"id": "79307b8a-91c3-49c8-b32a-c9f6fd7339fb",
"metadata": {},
"source": [
"## Lab 1 - Bézier Curves"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "1bd9e390-3bbe-4e58-9cae-943fbc6e6b49",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.special\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "47579be5-40e3-4cb4-83a3-39fb38d665f3",
"metadata": {},
"source": [
"### Task 1: Define a function to evaluate Bernstein Polynomials"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "89d3ec5b-a7be-4519-8787-f67ed2f7c2da",
"metadata": {},
"outputs": [],
"source": [
"def bernsteinPoly(t,i,n):\n",
" \"\"\"\n",
" This function evaluates the 'i'-th basis Bernstein Polynomial of order 'n' at the value 't'.\n",
" \"\"\"\n",
" binomCoeff = scipy.special.binom(n,i)\n",
" return binomCoeff * (t**i) * ((1-t)**(n-i))"
]
},
{
"cell_type": "markdown",
"id": "541422d8-84df-4dd8-a407-60774d58b459",
"metadata": {},
"source": [
"#### Plotting Quadratic Bernstein Polynomials"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "85dccf6e-e02a-44f6-b401-ade1c041ece1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(1)\n",
"plt.clf\n",
"\n",
"t = np.linspace(0,1,100)\n",
"c = [\"#F39237\",\"#D63230\",\"#40BCD8\",\"#944BBB\",\"#16C172\", \"#8DE969\",\"#FF2C55\",\"#B744B8\"]\n",
"\n",
"order = 2\n",
"\n",
"for i in range(0,order+1):\n",
" l = \"$b_{\"+str(i)+\",\"+str(order)+\"}$\"\n",
" plt.plot(t, bernsteinPoly(t,i,order), label=l, color=c[i % len(c)])\n",
"\n",
"plt.legend()\n",
"plt.grid(1)\n",
"plt.xlabel(\"$t$\")\n",
"plt.ylabel(\"$b_{i,n}(t)$\")\n",
"\n",
"plt.savefig('quadratic_bernstein.jpg')\n"
]
},
{
"cell_type": "markdown",
"id": "7c249fcf-f5b0-4365-b28b-76e8219bf40a",
"metadata": {},
"source": [
"#### Plotting Cubic Bernstein Polynomials"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b6a8d71b-770a-4bb0-9519-7efc32b9ba7b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(2)\n",
"plt.clf\n",
"\n",
"t = np.linspace(0,1,100)\n",
"c = [\"#F39237\",\"#D63230\",\"#40BCD8\",\"#944BBB\",\"#16C172\", \"#8DE969\",\"#FF2C55\",\"#B744B8\"]\n",
"\n",
"order = 3\n",
"\n",
"for i in range(0,order+1):\n",
" l = \"$b_{\"+str(i)+\",\"+str(order)+\"}$\"\n",
" plt.plot(t, bernsteinPoly(t,i,order), label=l, color=c[i % len(c)])\n",
"\n",
"plt.legend()\n",
"plt.grid(1)\n",
"plt.xlabel(\"$t$\")\n",
"plt.ylabel(\"$b_{i,n}(t)$\")\n",
"\n",
"plt.savefig('cubic_bernstein.jpg')\n"
]
},
{
"cell_type": "markdown",
"id": "6883bacc-48df-4b05-a4f7-b0c2fef195e5",
"metadata": {},
"source": [
"#### Plotting Higer Order Bernstein Polynomials"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e32dc5db-423e-4135-bb22-15da482ee3d1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(3)\n",
"plt.clf\n",
"\n",
"t = np.linspace(0,1,100)\n",
"c = [\"#F39237\",\"#D63230\",\"#40BCD8\",\"#944BBB\",\"#16C172\", \"#8DE969\",\"#FF2C55\",\"#B744B8\"]\n",
"\n",
"order = 20\n",
"\n",
"for i in range(0,order+1):\n",
" l = \"$b_{\"+str(i)+\",\"+str(order)+\"}$\"\n",
" plt.plot(t, bernsteinPoly(t,i,order), label=l, color=c[i % len(c)])\n",
"\n",
"#plt.legend()\n",
"plt.grid(1)\n",
"plt.xlabel(\"$t$\")\n",
"plt.ylabel(\"$b_{i,n}(t)$\")\n",
"\n",
"plt.savefig('higher2_bernstein.jpg')\n"
]
},
{
"cell_type": "markdown",
"id": "6e9747f0-547e-484a-8160-605a02229abe",
"metadata": {},
"source": [
"### Task 2: Create a function to compute a Bézier Curve"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "93ea6c5c-d72f-49c6-86d9-2c9182a8730b",
"metadata": {},
"outputs": [],
"source": [
"def bezierCurve(t,controlPoints):\n",
" '''\n",
" This function calculate the Beziér Curve coordinates given the list of parameters 't' and the 'controlPoints' of the curve.\n",
" '''\n",
" order = len(controlPoints)-1\n",
" \n",
" x_results = []\n",
" y_results = []\n",
" \n",
" for t_val in t:\n",
" x_sum = 0\n",
" y_sum = 0\n",
" for i in range(0,order+1):\n",
" control_x = controlPoints[i][0]\n",
" control_y = controlPoints[i][1]\n",
" x_sum += bernsteinPoly(t_val,i,order)*control_x\n",
" y_sum += bernsteinPoly(t_val,i,order)*control_y\n",
" x_results.append(x_sum)\n",
" y_results.append(y_sum) \n",
" \n",
" return [x_results,y_results]\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1a763450-5a67-4535-a3b5-b2fdff1caa3b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(4)\n",
"plt.clf\n",
"\n",
"\n",
"controlPoints = [[1,2], [4,5], [8,3],[10,4]]\n",
"\n",
"axes = plt.axes(label=3)\n",
"# axes.set_xlim(0,9)\n",
"# axes.set_ylim(0,6)\n",
"\n",
"plt.grid(1,zorder=0)\n",
"\n",
"t = np.linspace(0,1,100)\n",
"curve = bezierCurve(t,controlPoints)\n",
"\n",
"plt.plot(curve[0],curve[1], color=\"#000000\", zorder=1)\n",
"\n",
"for i in range(0,len(controlPoints)):\n",
" l = \"Control Point \"+str(i)\n",
" plt.scatter(controlPoints[i][0],controlPoints[i][1],color=c[i%len(c)],zorder=2, label=l)\n",
" \n",
"plt.legend(prop={'size': 7})\n",
" \n",
"plt.savefig('bezierCurve.jpg')\n"
]
}
],
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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