geometry/convex_polygon_contains.hpp

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "geometry/convex_polygon_contains.hpp"

Depends on

• geometry/base.hpp
• geometry/point.hpp
• geometry/polygon.hpp

Verified with

• test/verify/aoj-0412.test.cpp

Code

#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;
}
}  // namespace geometry

#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; }
}  // namespace geometry
#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>;
}  // namespace geometry
#line 2 "geometry/polygon.hpp"

#line 4 "geometry/polygon.hpp"

namespace geometry {
using Polygon = vector<Point>;
using Polygons = vector<Polygon>;
}  // namespace geometry
#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;
}
}  // namespace geometry

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