Update polygons.cpp

Geometry/polygons.cpp

@@ -1,63 +1,46 @@
 struct point {
-	int x, y;
+	ll x, y; // long long to avoid overflow problems
 	point() { x = y = 0; }
-	point(int _x, int _y) : x(_x), y(_y) {}
-	bool operator < (point p) const {
-		return (x == p.x && y < p.y) || x < p.x;
-	}
-	bool operator == (point p) const {
-		return x == p.x && y == p.y;
-	}
+	point(ll _x, ll _y) : x(_x), y(_y) {}
+	bool operator < (point p) const { return (x == p.x && y < p.y) || x < p.x; }
+	bool operator == (point p) const { return x == p.x && y == p.y; }
 };
 
-double dist(point& p1, point& p2) {
-	return hypot(p1.x - p2.x, p1.y - p2.y);
-}
+double dist(point& p1, point& p2) { return hypot(p1.x - p2.x, p1.y - p2.y); }
 
 struct vec {
-	int x, y;
-	vec(int _x, int _y) : x(_x), y(_y) {}
+	ll x, y;
+	vec(ll _x, ll _y) : x(_x), y(_y) {}
+	vec(point a, point b) { x = b.x - a.x, y = b.y - a.y; }
 };
 
-vec to_vec(point a, point b) {
-	return vec(b.x - a.x, b.y - a.y);
-}
+ll dot(vec a, vec b) { return a.x * b.x + a.y * b.y; }
 
-int dot(vec a, vec b) {
-	return (a.x * b.x + a.y * b.y);
-}
+ll norm_sq(vec v) { return v.x * v.x + v.y * v.y; }
 
-int norm_sq(vec v) {
-	return v.x * v.x + v.y * v.y;
-}
-
-int cross(vec a, vec b) {
-	return a.x * b.y - a.y * b.x;
-}
-
-bool ccw(point p, point q, point r) {
-	return cross(to_vec(p, q), to_vec(p, r)) > 0;
-}
+ll cross(vec a, vec b) { return a.x * b.y - a.y * b.x; }
 
 double angle(point a, point o, point b) {
-	vec oa = to_vec(o, a), ob = to_vec(o, b);
-	return acos(dot(oa, ob) / (sqrt(norm_sq(oa)) * sqrt(norm_sq(ob))));
+	vec oa(o, a), ob(o, b);
+	return acos(dot(oa, ob) / sqrt(norm_sq(oa) * norm_sq(ob)));
 }
 
+bool ccw(point p, point q, point r) { return cross(vec(p, q), vec(p, r)) > 0; }
+
 bool in_polygon(point pt, const vector<point>& P) {
 	double sum = 0;
 	for (int i = 0; i < P.size() - 1; i++) {
 		if (pt == P[i]) return true;
-		if (ccw(pt, P[i], P[i + 1])) sum += angle(P[i], pt, P[i + 1]);
-		else sum -= angle(P[i], pt, P[i + 1]);
+		ccw(pt, P[i], P[i + 1]) ? sum += angle(P[i], pt, P[i + 1]) : sum -= angle(P[i], pt, P[i + 1]);
 	}
 	return fabs(sum) > acos(-1.0);
 }
 
-double area(const vector<point>& P) {
-	int res = 0;
-	for (int i = 0; i < (int)P.size() - 1; i++)	res += (P[i].x * P[i + 1].y - P[i + 1].x * P[i].y);
-	return res / 2.0;
+ll area(const vector<point>& P) {
+	ll res = 0;
+	for (int i = 0; i < (int)P.size() - 1; i++) res += (P[i].x * P[i + 1].y - P[i + 1].x * P[i].y);
+	return res;
+	// return res / 2.0;
 }
 
 vector<point> convex_hull(vector<point>& P) {