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#include "geometry/distance_ss.hpp"

#include "segment.hpp" #include "is_intersect_ss.hpp" #include "distance_sp.hpp" namespace geometry { // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D Real distance_ss(const Segment &a, const Segment &b) { if(is_intersect_ss(a, b)) return 0; return min({distance_sp(a, b.a), distance_sp(a, b.b), distance_sp(b, a.a), distance_sp(b, a.b)}); } }

#line 2 "geometry/base.hpp" namespace geometry { using Real = double; const Real EPS = 1e-8; const Real PI = acos(static_cast< Real >(-1)); enum { OUT, ON, IN }; inline int sign(const Real &r) { return r <= -EPS ? -1 : r >= EPS ? 1 : 0; } inline bool equals(const Real &a, const Real &b) { return sign(a - b) == 0; } } #line 3 "geometry/point.hpp" namespace geometry { using Point = complex< Real >; istream &operator>>(istream &is, Point &p) { Real a, b; is >> a >> b; p = Point(a, b); return is; } ostream &operator<<(ostream &os, const Point &p) { return os << real(p) << " " << imag(p); } Point operator*(const Point &p, const Real &d) { return Point(real(p) * d, imag(p) * d); } // rotate point p counterclockwise by theta rad Point rotate(Real theta, const Point &p) { return Point(cos(theta) * real(p) - sin(theta) * imag(p), sin(theta) * real(p) + cos(theta) * imag(p)); } Real cross(const Point &a, const Point &b) { return real(a) * imag(b) - imag(a) * real(b); } Real dot(const Point &a, const Point &b) { return real(a) * real(b) + imag(a) * imag(b); } bool compare_x(const Point &a, const Point &b) { return equals(real(a), real(b)) ? imag(a) < imag(b) : real(a) < real(b); } bool compare_y(const Point &a, const Point &b) { return equals(imag(a), imag(b)) ? real(a) < real(b) : imag(a) < imag(b); } using Points = vector< Point >; } #line 3 "geometry/line.hpp" namespace geometry { struct Line { Point a, b; Line() = default; Line(const Point &a, const Point &b) : a(a), b(b) {} Line(const Real &A, const Real &B, const Real &C) { // Ax+By=C if(equals(A, 0)) { assert(!equals(B, 0)); a = Point(0, C / B); b = Point(1, C / B); } else if(equals(B, 0)) { a = Point(C / A, 0); b = Point(C / A, 1); } else { a = Point(0, C / B); b = Point(C / A, 0); } } friend ostream &operator<<(ostream &os, Line &l) { return os << l.a << " to " << l.b; } friend istream &operator>>(istream &is, Line &l) { return is >> l.a >> l.b; } }; using Lines = vector< Line >; } #line 3 "geometry/segment.hpp" namespace geometry { struct Segment : Line { Segment() = default; using Line::Line; }; using Segments = vector< Segment >; } #line 3 "geometry/ccw.hpp" namespace geometry { // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C constexpr int COUNTER_CLOCKWISE = +1; constexpr int CLOCKWISE = -1; constexpr int ONLINE_BACK = +2; // c-a-b constexpr int ONLINE_FRONT = -2; // a-b-c constexpr int ON_SEGMENT = 0; // a-c-b int ccw(const Point &a, Point b, Point c) { b = b - a, c = c - a; if(sign(cross(b, c)) == +1) return COUNTER_CLOCKWISE; if(sign(cross(b, c)) == -1) return CLOCKWISE; if(sign(dot(b, c)) == -1) return ONLINE_BACK; if(norm(b) < norm(c)) return ONLINE_FRONT; return ON_SEGMENT; } } #line 4 "geometry/is_intersect_ss.hpp" namespace geometry { bool is_intersect_ss(const Segment &s, const Segment &t) { return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0; } } #line 2 "geometry/projection.hpp" #line 5 "geometry/projection.hpp" namespace geometry { // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A Point projection(const Line &l, const Point &p) { auto t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b); return l.a + (l.a - l.b) * t; } } #line 4 "geometry/is_intersect_sp.hpp" namespace geometry { bool is_intersect_sp(const Segment &s, const Point &p) { return ccw(s.a, s.b, p) == ON_SEGMENT; } } #line 5 "geometry/distance_sp.hpp" namespace geometry { Real distance_sp(const Segment &s, const Point &p) { Point r = projection(s, p); if(is_intersect_sp(s, r)) return abs(r - p); return min(abs(s.a - p), abs(s.b - p)); } } #line 4 "geometry/distance_ss.hpp" namespace geometry { // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D Real distance_ss(const Segment &a, const Segment &b) { if(is_intersect_ss(a, b)) return 0; return min({distance_sp(a, b.a), distance_sp(a, b.b), distance_sp(b, a.a), distance_sp(b, a.b)}); } }