geometry/common_area_cp.hpp

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• Last update: 2024-04-24 02:34:04+09:00
• Include: #include "geometry/common_area_cp.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H

Depends on

• geometry/base.hpp
• geometry/ccw.hpp
• geometry/circle.hpp
• geometry/cross_point_cl.hpp
• geometry/distance_sp.hpp
• geometry/is_intersect_cs.hpp
• geometry/is_intersect_sp.hpp
• geometry/line.hpp
• geometry/point.hpp
• geometry/polygon.hpp
• geometry/projection.hpp
• geometry/segment.hpp

Verified with

• test/verify/aoj-cgl-7-h.test.cpp

Code

#include "base.hpp"
#include "point.hpp"
#include "polygon.hpp"
#include "distance_sp.hpp"
#include "cross_point_cl.hpp"
#include "is_intersect_cs.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
  Real ca_cp_impl(const Circle &c, const Point &a, const Point &b) {
    auto va = c.p - a, vb = c.p - b;
    Real f = cross(va, vb), ret = 0;
    if(sign(f) == 0) return ret;
    if(sign(max(abs(va), abs(vb)) - c.r) <= 0) return f;
    if(sign(distance_sp(Segment(a, b), c.p) - c.r) >= 0) return norm(c.r) * arg(vb * conj(va));
    auto tot = cross_point_cl(c, Line(a, b));
    if(is_intersect_cs(c, Segment(a, b)) != 2 and dot(a - tot[0], b - tot[0]) < 0) {
      swap(tot[0], tot[1]);
    }
    tot.emplace(begin(tot), a);
    tot.emplace_back(b);
    for(int i = 1; i < (int) tot.size(); i++) {
      ret += ca_cp_impl(c, tot[i - 1], tot[i]);
    }
    return ret;
  }

  Real common_area_cp(const Circle &c, const Polygon &p) {
    if(p.size() < 3) return 0;
    Real A = 0;
    for(int i = 0; i < p.size(); i++) {
      A += ca_cp_impl(c, p[i], p[(i + 1) % p.size()]);
    }
    return A * 0.5;
  }
}

#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 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 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;
  }
}
#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 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;
  }
}
#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));
  }
}
#line 3 "geometry/circle.hpp"

namespace geometry {
  struct Circle {
    Point p;
    Real r{};

    Circle() = default;

    Circle(const Point &p, const Real &r) : p(p), r(r) {}
  };

  using Circles = vector< Circle >;
}
#line 6 "geometry/cross_point_cl.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
  Points cross_point_cl(const Circle &c, const Line &l) {
    Point pr = projection(l, c.p);
    if(equals(abs(pr - c.p), c.r)) return {pr};
    Point e = (l.b - l.a) / abs(l.b - l.a);
    auto k = sqrt(norm(c.r) - norm(pr - c.p));
    return {pr - e * k, pr + e * k};
  }
}
#line 6 "geometry/is_intersect_cs.hpp"

namespace geometry {
  int is_intersect_cs(const Circle &c, const Segment &l) {
    Point h = projection(l, c.p);
    if(sign(norm(h - c.p) - norm(c.r)) > 0) return 0;
    auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
    if(sign(c.r - d1) >= 0 && sign(c.r - d2) >= 0) return 0;
    if(sign(c.r - d1) < 0 && sign(d2 - c.r) > 0 || sign(d1 - c.r) > 0 && sign(c.r - d2) < 0) return 1;
    if(sign(dot(l.a - h, l.b - h)) < 0) return 2;
    return 0;
  }
}
#line 7 "geometry/common_area_cp.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
  Real ca_cp_impl(const Circle &c, const Point &a, const Point &b) {
    auto va = c.p - a, vb = c.p - b;
    Real f = cross(va, vb), ret = 0;
    if(sign(f) == 0) return ret;
    if(sign(max(abs(va), abs(vb)) - c.r) <= 0) return f;
    if(sign(distance_sp(Segment(a, b), c.p) - c.r) >= 0) return norm(c.r) * arg(vb * conj(va));
    auto tot = cross_point_cl(c, Line(a, b));
    if(is_intersect_cs(c, Segment(a, b)) != 2 and dot(a - tot[0], b - tot[0]) < 0) {
      swap(tot[0], tot[1]);
    }
    tot.emplace(begin(tot), a);
    tot.emplace_back(b);
    for(int i = 1; i < (int) tot.size(); i++) {
      ret += ca_cp_impl(c, tot[i - 1], tot[i]);
    }
    return ret;
  }

  Real common_area_cp(const Circle &c, const Polygon &p) {
    if(p.size() < 3) return 0;
    Real A = 0;
    for(int i = 0; i < p.size(); i++) {
      A += ca_cp_impl(c, p[i], p[(i + 1) % p.size()]);
    }
    return A * 0.5;
  }
}

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