Update polygons.cpp

Changes

1 changed files (+21/-38)

• 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) {