geometry/distance_ss.hpp

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "geometry/distance_ss.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D

Depends on

• geometry/base.hpp
• geometry/ccw.hpp
• geometry/distance_sp.hpp
• geometry/is_intersect_sp.hpp
• geometry/is_intersect_ss.hpp
• geometry/line.hpp
• geometry/point.hpp
• geometry/projection.hpp
• geometry/segment.hpp

Verified with

• test/verify/aoj-cgl-2-d.test.cpp

Code

#include "distance_sp.hpp"
#include "is_intersect_ss.hpp"
#include "segment.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)});
}
}  // 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 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;
}
}  // namespace geometry
#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>;
}  // namespace geometry
#line 3 "geometry/segment.hpp"

namespace geometry {
struct Segment : Line {
  Segment() = default;

  using Line::Line;
};

using Segments = vector<Segment>;
}  // namespace geometry
#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;
}
}  // namespace geometry
#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;
}
}  // namespace geometry
#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));
}
}  // namespace geometry
#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;
}
}  // namespace geometry
#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)});
}
}  // namespace geometry

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