Update points_lines_vectors.cpp

Changes

1 changed files (+16/-50)

• Geometry/points_lines_vectors.cpp
  • @@ -1,56 +1,33 @@
    - #include <algorithm> - #include <iostream> - #include <climits> - #include <tuple> - #include <cmath> - using namespace std; constexpr auto EPS = numeric_limits<double>::epsilon(); struct point { int x, y; 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; - } + 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) {} + vec(point a, point b) { return vec(b.x - a.x, 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 (ll)a.x * b.x + (ll)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 (ll)v.x * v.x + (ll)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; - } + ll cross(vec a, vec b) { return (ll)a.x * b.y - (ll)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) * norm_sq(ob))); } - bool ccw(point p, point q, point r) { - return cross(to_vec(p, q), to_vec(p, r)) > 0; - } + bool ccw(point p, point q, point r) { return cross(to_vec(p, q), to_vec(p, r)) > 0; } double angle(point a, point o, point b) { vec oa = to_vec(o, a), ob = to_vec(o, b);
  • @@ -58,25 +35,16 @@ double angle(point a, point o, point b) {
    } struct line { - int a, b, c; - bool operator < (const line& l) const { - return tie(a, b, c) < tie(l.a, l.b, l.c); + ll a, b, c; + bool operator < (const line& l) const { return tie(a, b, c) < tie(l.a, l.b, l.c); } + line(point p1, point p2) { + ll a = p2.y - p1.y, b = p1.x - p2.x, c = p1.y * p2.x - p1.x * p2.y; + ll d = __gcd(__gcd(abs(a), abs(b)), abs(c)); + return { a / d, b / d, c / d }; } }; - int gcd(int a, int b) { - return b == 0 ? a : gcd(b, a % b); - } - - line to_line(point p1, point p2) { - int a = p2.y - p1.y, b = p1.x - p2.x, c = p1.y * p2.x - p1.x * p2.y; - int d = gcd(gcd(abs(a), abs(b)), abs(c)); - return { a / d, b / d, c / d }; - } - - double point_to_line(point p, line l) { - return abs(l.a * p.x + l.b * p.y + l.c) / hypot(l.a, l.b); - } + double point_to_line(point p, line l) { return abs(l.a * p.x + l.b * p.y + l.c) / hypot(l.a, l.b); } line perp_bi(point p1, point p2) { int a = 2 * (p2.x - p1.x), b = 2 * (p2.y - p1.y), c = -a * (p1.x + p2.x) / 2 - b * (p1.y + p2.y) / 2;
  • @@ -97,9 +65,7 @@ struct seg {
    seg(point _p1, point _p2) : p1(_p1), p2(_p2) {} }; - line to_line(seg s) { - return to_line(s.p1, s.p2); - } + line::line(seg s) { return to_line(s.p1, s.p2); } double point_to_seg(point p, seg s) { int a = norm_sq(to_vec(s.p1, s.p2)), b = norm_sq(to_vec(p, s.p1)), c = norm_sq(to_vec(p, s.p2));