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#include "geometry/convex_polygon_contains.hpp"
#include "base.hpp" #include "point.hpp" #include "polygon.hpp" namespace geometry { int convex_polygon_contains(const Polygon &Q, const Point &p) { int N = (int) Q.size(); Point g = (Q[0] + Q[N / 3] + Q[N * 2 / 3]) / 3.0; if(equals(imag(g), imag(p)) && equals(real(g), real(p))) return IN; Point gp = p - g; int l = 0, r = N; while(r - l > 1) { int mid = (l + r) / 2; Point gl = Q[l] - g; Point gm = Q[mid] - g; if(cross(gl, gm) > 0) { if(cross(gl, gp) >= 0 && cross(gm, gp) <= 0) r = mid; else l = mid; } else { if(cross(gl, gp) <= 0 && cross(gm, gp) >= 0) l = mid; else r = mid; } } r %= N; Real v = cross(Q[l] - p, Q[r] - p); return sign(v) == 0 ? ON : sign(v) == -1 ? OUT : IN; } }
#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 2 "geometry/polygon.hpp" #line 4 "geometry/polygon.hpp" namespace geometry { using Polygon = vector< Point >; using Polygons = vector< Polygon >; } #line 4 "geometry/convex_polygon_contains.hpp" namespace geometry { int convex_polygon_contains(const Polygon &Q, const Point &p) { int N = (int) Q.size(); Point g = (Q[0] + Q[N / 3] + Q[N * 2 / 3]) / 3.0; if(equals(imag(g), imag(p)) && equals(real(g), real(p))) return IN; Point gp = p - g; int l = 0, r = N; while(r - l > 1) { int mid = (l + r) / 2; Point gl = Q[l] - g; Point gm = Q[mid] - g; if(cross(gl, gm) > 0) { if(cross(gl, gp) >= 0 && cross(gm, gp) <= 0) r = mid; else l = mid; } else { if(cross(gl, gp) <= 0 && cross(gm, gp) >= 0) l = mid; else r = mid; } } r %= N; Real v = cross(Q[l] - p, Q[r] - p); return sign(v) == 0 ? ON : sign(v) == -1 ? OUT : IN; } }