hw-01: Fix floating point imprecision

homework-01-two-circles/main.c

@@ -1,23 +1,41 @@
 #include <bits/pthreadtypes.h>
-#include <stdio.h>
+#include <float.h>
-#include <stdlib.h>
 #include <math.h>
 #include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
 
 #ifdef __PROGTEST__
 #define debug(...) ((void)0)
 #else
-#define debug(fmt, ...) fprintf(stdout, "[%s:%d %s()] " fmt "\n", __FILE__, __LINE__, __func__, ##__VA_ARGS__)
+#define debug(fmt, ...)                                                        \
+  fprintf(stdout, "[%s:%d %s()] " fmt "\n", __FILE__, __LINE__, __func__,      \
+          ##__VA_ARGS__)
 #endif
 
+double clamp(double d) {
+  if (d > 1.0) {
+    return 1.0;
+  } else if (d < -1.0) {
+    return -1.0;
+  } else {
+    return d;
+  }
+}
+
 // https://www.geeksforgeeks.org/dsa/area-of-intersection-of-two-circles/
 double intersection_area(double a_r, double b_r, double distance) {
   double a_square = a_r * a_r;
   double b_square = b_r * b_r;
-	double distane_square = distance * distance;
+  double distance_square = distance * distance;
 
-	double alpha = acos((distane_square + a_square - b_square) / (2 * a_r * distance)) * 2;
+  double alpha_acos =
-	double beta = acos((distane_square + b_square - a_square) / (2 * b_r * distance)) * 2;
+      (distance_square + a_square - b_square) / (2 * a_r * distance);
+  double beta_acos =
+      (distance_square + b_square - a_square) / (2 * b_r * distance);
+
+  double alpha = acos(clamp(alpha_acos)) * 2;
+  double beta = acos(clamp(beta_acos)) * 2;
 
   double a1 = 0.5 * beta * b_square - 0.5 * b_square * sin(beta);
   double a2 = 0.5 * alpha * a_square - 0.5 * a_square * sin(alpha);
@@ -29,12 +47,11 @@ double intersection_area(double a_r, double b_r, double distance) {
   return area;
 }
 
-double circle_area(double radius) {
+double circle_area(double radius) { return M_PI * radius * radius; }
-	return M_PI * radius * radius;
-}
 
 int main() {
-	double a_center_x = 0, a_center_y = 0, a_radius = 0, b_center_x = 0, b_center_y = 0, b_radius = 0;
+  double a_center_x = 0, a_center_y = 0, a_radius = 0, b_center_x = 0,
+         b_center_y = 0, b_radius = 0;
 
   printf("Zadejte parametry kruznice #1:\n");
 
@@ -52,33 +69,68 @@ int main() {
     return EXIT_FAILURE;
   }
 
+  double center_distance =
+      sqrt((b_center_x - a_center_x) * (b_center_x - a_center_x) +
+           (b_center_y - a_center_y) * (b_center_y - a_center_y));
 
-	double center_distance = sqrt((b_center_x - a_center_x) * (b_center_x - a_center_x) + (b_center_y - a_center_y) * (b_center_y - a_center_y));
+  debug("Distance of centers = %0.60lf", center_distance);
+  debug("Radii difference = %0.60lf", a_radius - b_radius);
+  debug("Radii difference = %0.60lf", b_radius - a_radius);
+  debug("Center + #1 = %0.60lf", a_center_x + a_radius);
+  debug("Center + #2 = %0.60lf", b_center_x + b_radius);
 
   double radii_sum = a_radius + b_radius;
-	if(a_center_x == b_center_x && a_center_y == b_center_y && a_radius == b_radius) {
+  double radii_difference = fabs(a_radius - b_radius);
+  double epsilon = 100 * DBL_EPSILON * fmax(a_radius, b_radius);
+
+  // Both origin points and radii are identical
+  bool are_identical = a_center_x == b_center_x && a_center_y == b_center_y && a_radius == b_radius;
+
+  // d = r1 + r2
+  // d - r1 - r1 < epsilon
+  bool are_touching_from_outside = fabs(center_distance - radii_sum) < epsilon;
+
+  // d = |r1 - r2|
+  // d - |r1 - r2| < epsilon
+  bool are_touching_from_inside = fabs(center_distance - radii_difference) < epsilon;
+
+  // d < |r1 - r2|
+  bool is_fully_inside = center_distance < radii_difference;
+
+  // d < r1 + r2
+  bool are_overlapping = center_distance < radii_sum;
+
+  if (are_identical) {
     printf("Kruznice splyvaji, prekryv: %lf\n", circle_area(a_radius));
-	} else if(center_distance <= a_radius - b_radius) {
-		debug("B radius = %0.60lf", b_radius);
-		debug("Double A radius = %0.60lf", a_radius * 2);
-		if(center_distance + b_radius == a_radius) {
-			printf("Vnitrni dotyk, kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n", circle_area(b_radius));
-		} else {
-			printf("Kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n", circle_area(b_radius));
   }
-	} else if(center_distance <= b_radius - a_radius) {
+  else if (are_touching_from_inside) {
-		debug("A radius = %0.60lf", a_radius);
+    if (a_radius > b_radius) {
-		debug("Double B radius = %0.60lf", b_radius * 2);
+      printf(
-		if(center_distance + a_radius == b_radius) {
+          "Vnitrni dotyk, kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n",
-			printf("Vnitrni dotyk, kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n", circle_area(a_radius));
+          circle_area(b_radius));
     } else {
-			printf("Kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n", circle_area(a_radius));
+      printf(
+          "Vnitrni dotyk, kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n",
+          circle_area(a_radius));
     }
-	} else if(center_distance < radii_sum) {
+  }
-		printf("Kruznice se protinaji, prekryv: %lf\n", intersection_area(a_radius, b_radius, center_distance));
+  else if (are_touching_from_outside) {
-	} else if(center_distance == radii_sum) {
     printf("Vnejsi dotyk, zadny prekryv.\n");
+  }
+  else if (is_fully_inside) {
+    if (a_radius > b_radius) {
+      printf("Kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n",
+             circle_area(b_radius));
     } else {
+      printf("Kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n",
+             circle_area(a_radius));
+    }
+  }
+  else if (are_overlapping) {
+    printf("Kruznice se protinaji, prekryv: %lf\n",
+           intersection_area(a_radius, b_radius, center_distance));
+  }
+  else {
     printf("Kruznice lezi vne sebe, zadny prekryv.\n");
   }