Add circle

Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>

algorithms/geometry/circle.cpp

+/// Circle
+
+struct Circle {
+  Point<double> c;
+  double r;
+
+  Circle(Point<double> c, double r) : c(c), r(r) {}
+
+  // Circumcircle
+  Circle(Point<double> a, Point<double> b, Point<double> c) {
+    Point<double> u((b - a).y, -(b - a).x);
+    Point<double> v((c - a).y, -(c - a).x);
+    Point<double> n = (c - b)*0.5;
+
+    double t = u.cross(n) / v.cross(u);
+
+    this->c = (a + c)*0.5 + v*t;
+    this->r = dist(this->c, a);
+  }
+
+  bool contains(Point<double> p) {
+    return (dist(c, p) <= r + EPS);
+  }
+};
+
+// Minumum enclosing circle
+Circle min_enclosing(vector<Point<double>> p) {
+  random_shuffle(all(p));
+  Circle C(p[0], 0.0);
+
+  for (int i = 0; i < p.size(); ++i) {
+    if (C.contains(p[i])) continue;
+    C = Circle(p[i], 0.0);
+
+    for (int j = 0; j < i; ++j) {
+      if (C.contains(p[j])) continue;
+      C = Circle((p[j] + p[i])*0.5, 0.5*dist(p[j], p[i]));
+
+      for (int k = 0; k < j; ++k) {
+        if (C.contains(p[k])) continue;
+        C = Circle(p[j], p[i], p[k]);
+      }
+    }
+  }
+
+  return C;
+}

algorithms/geometry/geometry_primitives.cpp

@@ -12,6 +12,7 @@ struct Point {
 
   Point operator+(Point p) { return Point(x+p.x, y+p.y); }
   Point operator-(Point p) { return Point(x-p.x, y-p.y); }
+  Point operator*(T s) { return Point(x*s, y*s); }
 
   T dot(Point p)   { return (x*p.x) + (y*p.y); }
   T cross(Point p) { return (x*p.y) - (y*p.x); }
@@ -51,6 +52,10 @@ struct Point {
   }
 };
 
+double dist(Point<double> a, Point<double> b) {
+  return hypot(a.x - b.x, a.y - b.y);
+}
+
 template <typename T>
 struct Segment {
   Point<T> a, b;