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69c4a980 · cprutean · 376e9177 · 69c4a980
Commit 69c4a980 authored 1 year ago by cprutean
--- a/CodeExamples/SphereVolume.ipynb
+++ b/CodeExamples/SphereVolume.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "227f88f0",
+   "metadata": {},
+   "source": [
+    "# Sphere Volume"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "695f4dd5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "   Program to estimate the volume of a sphere by counting the\n",
+    "   number of random points that fall inside compared with the\n",
+    "   number of points in a box round the sphere.\n",
+    "\"\"\"\n",
+    "import math\n",
+    "import random\n",
+    "\n",
+    "\n",
+    "def random_point(max_range):\n",
+    "    \"\"\"\n",
+    "    Return a random 3d point in range +/max_range\n",
+    "    \"\"\"\n",
+    "    x = random.uniform(-max_range,max_range)\n",
+    "    y = random.uniform(-max_range,max_range)\n",
+    "    z = random.uniform(-max_range,max_range)\n",
+    "\n",
+    "    return x,y,z\n",
+    "\n",
+    "def point_in_sphere(radius,x,y,z):\n",
+    "    \"\"\"\n",
+    "    Check if a point is within a sphere specified.\n",
+    "    \"\"\"\n",
+    "    if x*x + y*y + z*z <= radius*radius:\n",
+    "        return True\n",
+    "    else :\n",
+    "        return False\n",
+    "\n",
+    "def main():\n",
+    "    \"\"\"\n",
+    "    Main program\n",
+    "    \"\"\"\n",
+    "    \n",
+    "    points = int(input(\"Number of points : \"))        # Ask for initial conditions\n",
+    "    radius = float(input(\"Radius of sphere : \"))\n",
+    "    \n",
+    "    #               Counters for number inside and look variable\n",
+    "    inside, p  = 0 , 0\n",
+    "    while p <= points:                     # Loop over number of trial points\n",
+    "        x,y,z = random_point(radius)       # Random point in cube round sphere\n",
+    "        if point_in_sphere(radius,x,y,z) : # Is it inside, if so count it\n",
+    "            inside += 1\n",
+    "        p += 1 \n",
+    "\n",
+    "    #         Estimated volume is given by ratio of number of points inside\n",
+    "    #         times volume of cube round sphere\n",
+    "    #\n",
+    "    estimate = float(inside)/float(points)*math.pow(2*radius,3)\n",
+    "    vol = 4.0*math.pi*math.pow(radius,3)/3.0\n",
+    "\n",
+    "    print(\"Estimate volume is : \" + str(estimate) + \" real volume is : \" + str(vol))\n",
+    "\n",
+    "\n",
+    "main()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+%% Cell type:markdown id:227f88f0 tags:
+
+# Sphere Volume
+
+%% Cell type:code id:695f4dd5 tags:
+
+``` python
+"""
+   Program to estimate the volume of a sphere by counting the
+   number of random points that fall inside compared with the
+   number of points in a box round the sphere.
+"""
+import math
+import random
+
+
+def random_point(max_range):
+    """
+    Return a random 3d point in range +/max_range
+    """
+    x = random.uniform(-max_range,max_range)
+    y = random.uniform(-max_range,max_range)
+    z = random.uniform(-max_range,max_range)
+
+    return x,y,z
+
+def point_in_sphere(radius,x,y,z):
+    """
+    Check if a point is within a sphere specified.
+    """
+    if x*x + y*y + z*z <= radius*radius:
+        return True
+    else :
+        return False
+
+def main():
+    """
+    Main program
+    """
+
+    points = int(input("Number of points : "))        # Ask for initial conditions
+    radius = float(input("Radius of sphere : "))
+
+    #               Counters for number inside and look variable
+    inside, p  = 0 , 0
+    while p <= points:                     # Loop over number of trial points
+        x,y,z = random_point(radius)       # Random point in cube round sphere
+        if point_in_sphere(radius,x,y,z) : # Is it inside, if so count it
+            inside += 1
+        p += 1
+
+    #         Estimated volume is given by ratio of number of points inside
+    #         times volume of cube round sphere
+    #
+    estimate = float(inside)/float(points)*math.pow(2*radius,3)
+    vol = 4.0*math.pi*math.pow(radius,3)/3.0
+
+    print("Estimate volume is : " + str(estimate) + " real volume is : " + str(vol))
+
+
+main()
+```