Create points_lines_vectors.cpp

Changes

1 changed files (+107/-0)

• Geometry/points_lines_vectors.cpp (new)
  • @@ -0,0 +1,107 @@
    + #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; + } + }; + + 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 to_vec(point a, point b) { + return vec(b.x - a.x, b.y - a.y); + } + + int dot(vec a, vec b) { + return (a.x * b.x + a.y * b.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; + } + + 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)))); + } + + struct line { + int a, b, c; + bool operator < (const line& l) const { + return tie(a, b, c) < tie(l.a, l.b, l.c); + } + }; + + int gcd(int a, int b) { + return b == 0 ? a : gcd(b, a % b); + } + + line points_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); + } + + 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; + int d = gcd(gcd(abs(a), abs(b)), abs(c)); + return { a / d, b / d, c / d }; + } + + point reflect(point p, line l) { + int x = p.x * (l.b * l.b - l.a * l.a) - 2 * l.a * (l.b * p.y + l.c); + int y = p.y * (l.a * l.a - l.b * l.b) - 2 * l.b * (l.a * p.x + l.c); + int d = l.a * l.a + l.b * l.b; + if (x % d && y % d) return { 10001, 10001 }; + else return { x / d, y / d }; + } + + struct seg { + point p1, p2; + seg(point _p1, point _p2) : p1(_p1), p2(_p2) {} + }; + + line seg_to_line(seg s) { + return points_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)); + if (a + b > c && a + c > b) return point_to_line(p, seg_to_line(s)); + else return min(dist(p, s.p1), dist(p, s.p2)); + } + + bool seg_isect(seg a, seg b) { + return ccw(a.p1, a.p2, b.p1) * ccw(a.p1, a.p2, b.p2) <= 0 && ccw(b.p1, b.p2, a.p1) * ccw(b.p1, b.p2, a.p2) <= 0); + }