geometry/is_intersect_ss.hpp

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Last update: 2022-09-11 00:53:50+09:00
Include: #include "geometry/is_intersect_ss.hpp"

Depends on

Required by

geometry/distance_ss.hpp

Verified with

Code

#include "point.hpp"
#include "ccw.hpp"
#include "segment.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/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;
  }
}
#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 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;
  }
}