circles.cpp

#include <bits/stdc++.h>
using namespace std;

double DEG_to_RAD(double d) { return d*M_PI/180.0; }

double RAD_to_DEG(double r) { return r*180.0/M_PI; }

struct point_i {
  int x, y;                                      // use this if possible
  point_i() { x = y = 0; }                       // default constructor
  point_i(int _x, int _y) : x(_x), y(_y) {}      // constructor
};

struct point {
  double x, y;                                   // if need more precision
  point() { x = y = 0.0; }                       // default constructor
  point(double _x, double _y) : x(_x), y(_y) {}  // constructor
};

int insideCircle(point_i p, point_i c, int r) {  // all integer version
  int dx = p.x-c.x, dy = p.y-c.y;
  int Euc = dx*dx + dy*dy, rSq = r*r;            // all integer
  return Euc < rSq ? 1 : Euc == rSq ? 0 : -1;    // inside/border/outside
}

bool circle2PtsRad(point p1, point p2, double r, point &c) {
  // to get the other center, reverse p1 and p2
  double d2 = (p1.x-p2.x) * (p1.x-p2.x) + 
              (p1.y-p2.y) * (p1.y-p2.y);
  double det = r*r / d2 - 0.25;
  if (det < 0.0) return false;
  double h = sqrt(det);
  c.x = (p1.x+p2.x) * 0.5 + (p1.y-p2.y) * h;
  c.y = (p1.y+p2.y) * 0.5 + (p2.x-p1.x) * h;
  return true;
}

int main() {
  // circle equation, inside, border, outside
  point_i pt(2, 2);
  int r = 7;
  point_i inside(8, 2);
  printf("%d\n", insideCircle(inside, pt, r));   // 1, inside
  point_i border(9, 2);
  printf("%d\n", insideCircle(border, pt, r));   // 0, at border
  point_i outside(10, 2);
  printf("%d\n", insideCircle(outside, pt, r));  // -1, outside

  double d = 2*r;
  printf("Diameter = %.2lf\n", d);
  double c = M_PI*d;
  printf("Circumference (Perimeter) = %.2lf\n", c);
  double A = M_PI*r*r;
  printf("Area of circle = %.2lf\n", A);

  printf("Length of arc   (central angle = 60 degrees) = %.2lf\n", 60.0/360.0 * c);
  printf("Length of chord (central angle = 60 degrees) = %.2lf\n", sqrt((2*r*r) * (1 - cos(DEG_to_RAD(60.0)))));
  printf("Area of sector  (central angle = 60 degrees) = %.2lf\n", 60.0/360.0 * A);

  point p1;
  point p2(0.0, -1.0);
  point ans;
  circle2PtsRad(p1, p2, 2.0, ans);
  printf("One of the center is (%.2lf, %.2lf)\n", ans.x, ans.y);
  circle2PtsRad(p2, p1, 2.0, ans);               // reverse p1 with p2
  printf("The other center  is (%.2lf, %.2lf)\n", ans.x, ans.y);

  return 0;
}