/*
 * file: a1.c

 * Solution to assignment 1, CSC 270, Fall 99

 * Program extends the rectangle, midpoint and trapezoid rules
 * to approximate 3D integration.  
 */

#include <stdio.h>
#include "func.h"

/*
 * Rectangle rule
 */

float rectangle (float minx, float maxx, float miny, float maxy)
{
   return (maxx - minx) * (maxy - miny) * func(minx, miny);
}

/* 
 * Midpoint rule
 */

float midpoint (float minx, float maxx, float miny, float maxy)
{
   return (maxx - minx) * (maxy - miny) * func((minx + maxx) / 2, (miny +
      maxy) / 2);
}

/*
 * Trapezoid rule
 */

float trapezoid (float minx, float maxx, float miny, float maxy)
{
   return ((maxx - minx) * (maxy - miny) * (func(minx, miny) + func(maxx,
      miny)) / 2);
}

/*
 * Composite rule calculates the size of the rectangular intervals.
 * Sums the volume of the individual intervals.
 */

float composite (float ff (float, float, float, float), float minx, float
maxx, float miny, float maxy, int nxintervals, int nyintervals)
{
   float xwidth = (maxx - minx) / (float) nxintervals;
   float ywidth = (maxy - miny) / (float) nyintervals;
   float volume = 0.0;
   int xcount;
   int ycount;

   for (xcount = 0; xcount < nxintervals; xcount++)
      for (ycount = 0; ycount < nyintervals; ycount++)
      {
         volume += (*ff) (minx + xwidth * xcount, minx + xwidth * (xcount 
            + 1), miny + ywidth * ycount, miny + ywidth * (ycount + 1));
      }
   
   return volume;
}

/*
 * Reads the integral range and number of subintervals.
 * Reports the results for the three different rules.
 */

main ()
{
   float xmin, xmax, ymin, ymax;
   float volumeRectangle, volumeMidpoint, volumeTrapezoid;   
   int xIntervals, yIntervals;

   printf ("input integral range for x values, minimum x value, maximum x value\n");
   scanf ("%f%f", &xmin, &xmax);
   printf ("input integral range for y values, minimum y value, maximum y value\n");
   scanf ("%f%f", &ymin, &ymax);
   printf ("input the number of intervals in the x direction\n");
   scanf ("%d", &xIntervals);
   printf ("input the number of intervals in the y direction\n");
   scanf ("%d", &yIntervals);

   volumeRectangle = composite (rectangle, xmin, xmax, ymin, ymax,
      xIntervals, yIntervals);
   volumeMidpoint = composite (midpoint, xmin, xmax, ymin, ymax,
      xIntervals, yIntervals);
   volumeTrapezoid = composite (trapezoid, xmin, xmax, ymin, ymax,
      xIntervals, yIntervals);

   printf ("rectangle %f\n", volumeRectangle);
   printf ("midpoint %f\n", volumeMidpoint);
   printf ("trapezoid %f\n", volumeTrapezoid);
}