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  1. // Project 1
  2. // CMSC 15200
  3. // Winter 2011
  4. // Miranda Seitz-McLeese
  5. // mseitzmcleese@uchicago.edu
  6.  
  7. #include <math.h>
  8. #include <stdio.h>
  9.  
  10. // Recursion boundaries
  11. #define max_levels 30
  12. #define min_levels 3
  13.  
  14. // Global variable for accounting of evaluations
  15. int evaluations = 0;
  16.  
  17. // Point struct definition
  18. struct point
  19. {
  20.         double x;
  21.         double y;
  22. };
  23.  
  24. // Pointer to a function that takes a double and returns a point
  25. typedef struct point (*pcurve)(double);
  26.  
  27. // Distance between two points.
  28. double distance (struct point p_one, struct point p_two);
  29.  
  30. // Line
  31. struct point line(double t);
  32.  
  33. // Parabola
  34. struct point parabola(double t);
  35.  
  36. // Sqrt Sine
  37. struct point sine(double t);
  38.  
  39. // Recursive function to find curve length
  40. double curve_length(double left, double right, pcurve curve, double tolerance);
  41.  
  42. // Print a few test results of curve_length
  43. int main()
  44. {
  45.         // Declarations
  46.         double line_length, parabola_length, sine_length;  // variables to hold the results of curve_length
  47.        
  48.         // Line results
  49.         line_length = curve_length(0, 2, line, .01);
  50.         printf("Line     (tol = .01)   : %f, %d evaluations \n", line_length, evaluations);
  51.         evaluations = 0;
  52.         line_length = curve_length(0, 2, line, .0001);
  53.         printf("         (tol = .0001) : %f, %d evaluations \n", line_length, evaluations);
  54.         evaluations = 0;
  55.        
  56.         // Parabola results
  57.         parabola_length = curve_length(0, 1, parabola, .01);
  58.         printf("Parabola (tol = .01)   : %f, %d evaluations \n", parabola_length, evaluations);
  59.         evaluations = 0;
  60.         line_length = curve_length(0, 1, parabola, .0001);
  61.         printf("         (tol = .0001) : %f, %d evaluations \n", parabola_length, evaluations);
  62.         evaluations = 0;
  63.        
  64.         // Sine Results
  65.         sine_length = curve_length(0, 1, sine, .01);
  66.         printf("Sine     (tol = .01)   : %f, %d evaluations \n", sine_length, evaluations);
  67.         evaluations = 0;
  68.         sine_length = curve_length(0, 1, sine, .0001);
  69.         printf("         (tol = .0001) : %f, %d evaluations \n", sine_length, evaluations);
  70.         return 0;
  71. }
  72.  
  73. double distance(struct point p_one, struct point p_two)
  74. {
  75.         double dist = sqrt((p_one.x - p_two.x)*(p_one.x - p_two.x) + (p_one.y - p_two.y)*(p_one.y - p_two.y));
  76.         return dist;
  77. }
  78.  
  79. struct point line(double t)
  80. {
  81.         struct point p;
  82.         p.x = t;
  83.         p.y = 2*t;
  84.         return p;
  85. }
  86.  
  87. struct point parabola(double t)
  88. {
  89.         struct point p;
  90.         p.x = t;
  91.         p.y = t*t;
  92.         return p;
  93. }
  94.  
  95. struct point sine(double t)
  96. {
  97.         struct point p;
  98.         p.x = t;
  99.         p.y = sqrt(sin(t));
  100.         return p;
  101. }
  102.  
  103. double curve_length(double left, double right, pcurve curve, double tolerance)
  104. {
  105.         // Declarations
  106.         static int levels = 0;           // Keep track of levels of recursion
  107.         double corse, fine;              // Estimation variables
  108.         double middle;                   // Mid point of interval
  109.         double first_half, second_half;  // To hold the results of the recursive call
  110.        
  111.         // Increment bookkeeping variables.
  112.         levels++;
  113.         evaluations++;
  114.        
  115.         // Calculate midpoint
  116.         middle = left + fabs(right - left)/2;
  117.        
  118.         // Calculate corse and fine estimates
  119.         corse = distance((curve(left)), (curve(right)));
  120.         fine = distance(curve(left), curve(middle)) + distance(curve(middle), curve(right));
  121.        
  122.         // If precise enough, return the fine value, if not, recurse again.
  123.         if (levels >= max_levels)
  124.         {
  125.                 levels--;
  126.                 return fine;
  127.         }
  128.         if (levels < min_levels || fabs(fine-corse) > tolerance){
  129.                 first_half = curve_length(left, middle, curve, (tolerance/2));
  130.                 second_half = curve_length(middle, right, curve, (tolerance/2));
  131.                 levels--;
  132.                 return (first_half + second_half);
  133.         }
  134.         else {
  135.                 levels--;
  136.                 return fine;
  137.         }
  138. }
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