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#include "geometry/ccw.hpp"

#pragma once #include "point.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 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/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; } }