SOURCE FILE: 7.07AreaEstimator.cpp

//   
// Example 7.7. Program to estimate the area under a curve 
// using the dartboard method   
//    
   
#include <iostream.h>
#include <math.h>   
#include "RandDef.h"   
   
const int NUMDARTS = 1000;     // number of darts to throw 
const float SMALLEST_X = 0.0;  // smallest x value 
const float LARGEST_X = 2.0;   // largest x value 
const float MAX_Y = 1.5;       // upper bound of y values 
   
int main(void)   
{   
   int  CountHitsBelow(void);   
   
   int   NumHitsBelow;         // number of darts below curve    
   float AreaOfRectangle,      // area of rectangular dartboard 
         EstimatedArea;        // estimated area under curve     
   
   SeedRand();   
      
   NumHitsBelow    = CountHitsBelow();   
   AreaOfRectangle = (LARGEST_X - SMALLEST_X) * MAX_Y;   
   EstimatedArea   = AreaOfRectangle * NumHitsBelow / NUMDARTS;   
      
   cout << "Estimated area under curve from " << SMALLEST_X   
        << " to " << LARGEST_X << " is " << EstimatedArea << endl;
   
   return 0;
}   
   
//   
// Function to throw darts and return number of hits below curve   
// Pre:  none   
// Post: The number of darts hitting below curve was returned.   
//    
   
int CountHitsBelow(void)   
{   
   float f(float x);   
   
   int   NumHitsBelow = 0;  // number of darts below curve 
   float randomX,     // random x between SMALLEST_X & LARGEST_X 
         randomY,     // random y between 0 & MaxY 
         f_of_x;      // f(x) 
   
   for (int i = 0; i < NUMDARTS; i++)   
   {   
      randomX = random_double_range(SMALLEST_X, LARGEST_X);   
      randomY = random_double_range(0, MAX_Y);   
      f_of_x = f(randomX);   
      if (randomY < f_of_x)   
         NumHitsBelow++;               
   }   
   return NumHitsBelow;   
}   
   
//   
// A mathematical function   
// Pre:  x is a floating point number.   
// Post: The square root of ((cos(x))^2 + 1) was returned.   
//    
   
float f(float x)   
{   
   return (sqrt(cos(x) * cos(x) + 1));   
}