comp-geometry

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub Luzhiled/comp-geometry

:heavy_check_mark: test/aoj/cgl/7_H.test.cpp

Depends on

Code

// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_H
// verification-helper: ERROR 0.000001

#include "src/real-geometry/area/common-area-circle-polygon.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/class/circle.hpp"
#include "src/real-geometry/class/polygon.hpp"
#include "src/real-geometry/utility/io-set.hpp"

#include <iostream>

int main() {
  using R = long double;

  int n;
  R r;
  std::cin >> n >> r;

  geometry::circle<R> c({0, 0}, r);

  geometry::polygon<R> poly(n);
  for (auto &p : poly) std::cin >> p;

  std::cout << geometry::common_area_circle_polygon(c, poly) << std::endl;
}
#line 1 "test/aoj/cgl/7_H.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_H
// verification-helper: ERROR 0.000001

#line 2 "src/real-geometry/area/common-area-circle-polygon.hpp"

#line 2 "src/real-geometry/class/circle.hpp"

#line 2 "src/real-geometry/class/point.hpp"

#line 2 "src/real-geometry/class/vector.hpp"

#include <complex>
#include <iostream>

namespace geometry {

  template< typename R >
  class vec2d : public std::complex< R > {
    using complex = std::complex< R >;

   public:
    using complex::complex;

    vec2d(const complex &c): complex::complex(c) {}

    const R x() const { return this->real(); }
    const R y() const { return this->imag(); }

    friend vec2d operator*(const vec2d &v, const R &k) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend vec2d operator*(const R &k, const vec2d &v) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend std::istream &operator>>(std::istream &is, vec2d &v) {
      R x, y;
      is >> x >> y;
      v = vec2d(x, y);
      return is;
    }
 
  };

}
#line 4 "src/real-geometry/class/point.hpp"

#include <vector>

namespace geometry {

  template< typename R >
  using point = vec2d<R>;

  template< typename R >
  using points = std::vector< point< R > >;

}
#line 4 "src/real-geometry/class/circle.hpp"

#line 6 "src/real-geometry/class/circle.hpp"

// circle
namespace geometry {

  template< typename R >
  class circle {
   public:
    point<R> o;
    R r;

    circle() = default;
    circle(point<R> o, R r) : o(o), r(r) {}

    const point<R> center() const {
      return o;
    }

    const R radius() const {
      return r;
    }
  };


  template< typename R >
  using circles = std::vector< circle<R> >;

}
#line 2 "src/real-geometry/class/polygon.hpp"

#line 4 "src/real-geometry/class/polygon.hpp"

#line 6 "src/real-geometry/class/polygon.hpp"

namespace geometry {

  template< typename R >
  using polygon = std::vector< point<R> >;

  template< typename R >
  using polygons = std::vector< polygon<R> >;

}
#line 2 "src/real-geometry/class/segment.hpp"

#line 2 "src/real-geometry/utility/equals/vector.hpp"

#line 2 "src/real-geometry/utility/equals/real-number.hpp"

#line 2 "src/real-geometry/utility/sign.hpp"

#line 2 "src/real-geometry/common/const/eps.hpp"

#line 2 "src/real-geometry/common/float-alias.hpp"

namespace geometry {

  using f80 = long double;
  using f64 = double;

}
#line 4 "src/real-geometry/common/const/eps.hpp"

namespace geometry {

  inline static f80 &eps() {
    static f80 EPS = 1e-10;
    return EPS;
  }

  void set_eps(f80 EPS) {
    eps() = EPS;
  }

}
#line 2 "src/real-geometry/numbers/sign.hpp"

#line 2 "src/real-geometry/common/int-alias.hpp"

namespace geometry {

  using i32 = int;
  using i64 = long long;

}
#line 4 "src/real-geometry/numbers/sign.hpp"

namespace geometry::number::sign {

  constexpr i32 PLUS  = +1;
  constexpr i32 ZERO  =  0;
  constexpr i32 MINUS = -1;

}
#line 5 "src/real-geometry/utility/sign.hpp"

namespace geometry {

  using namespace geometry::number::sign;

  template< typename R >
  inline int sign(R r) {
    if (r < -eps()) return MINUS;
    if (r > +eps()) return PLUS;
    return ZERO;
  }

}
#line 4 "src/real-geometry/utility/equals/real-number.hpp"

namespace geometry {

  template< typename R >
  bool equals(R a, R b) {
    return sign(a - b) == 0;
  }

}
#line 5 "src/real-geometry/utility/equals/vector.hpp"

namespace geometry {

  template< typename R >
  bool equals(const vec2d<R> &a, const vec2d<R> &b) {
    return equals(a.x(), b.x()) and equals(a.y(), b.y());
  }

}
#line 5 "src/real-geometry/class/segment.hpp"

#include <cassert>
#line 8 "src/real-geometry/class/segment.hpp"

namespace geometry {

  template< typename R >
  class segment {
   public:
    point<R> a, b;

    segment() = default;
    segment(point<R> a, point<R> b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using segments = std::vector< segment<R> >;

}
#line 2 "src/real-geometry/common/size-alias.hpp"

#include <cstddef>

namespace geometry {

  using isize = std::ptrdiff_t;
  using usize = std::size_t;

}
#line 2 "src/real-geometry/cross-point/cross-point-cl.hpp"

#line 2 "src/real-geometry/class/line.hpp"

#line 5 "src/real-geometry/class/line.hpp"

#line 8 "src/real-geometry/class/line.hpp"

namespace geometry {

  template< typename R >
  class line {
    using P = point<R>;

   public:
    P a, b;

    line() = default;
    line(P a, P b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using lines = std::vector< line<R> >;

}
#line 2 "src/real-geometry/mapping/projection.hpp"

#line 2 "src/real-geometry/operation/inner-product.hpp"

#line 4 "src/real-geometry/operation/inner-product.hpp"

namespace geometry {

  template< typename R >
  R inner_product(const vec2d<R> &a, const vec2d<R> &b) {
    return a.x() * b.x() + a.y() * b.y();
  }

}
#line 6 "src/real-geometry/mapping/projection.hpp"

#line 8 "src/real-geometry/mapping/projection.hpp"

namespace geometry {

  template< typename R >
  point<R> projection(const line<R> &l, const point<R> &p) {
    R t = inner_product<R>(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
    return l.a + (l.a - l.b) * t;
  }

}
#line 7 "src/real-geometry/cross-point/cross-point-cl.hpp"

#include <cmath>
#line 10 "src/real-geometry/cross-point/cross-point-cl.hpp"

namespace geometry {

  template< typename R >
  points<R> cross_point_cl(const circle<R> &c, const line<R> &l) {
    point<R> pr = projection(l, c.center());

    R d = std::norm(c.radius()) - std::norm(pr - c.center());

    if (sign(d) == -1) {
      return {};
    }
    if (sign(d) == 0) {
      return {pr};
    }

    point<R> e = (l.b - l.a) / std::abs(l.b - l.a);
    R k = std::sqrt(d);
    return {pr + e * k, pr - e * k};
  }

}
#line 2 "src/real-geometry/distance/distance-sp.hpp"

#line 2 "src/real-geometry/operation/ccw.hpp"

#line 2 "src/real-geometry/numbers/ccw.hpp"

namespace geometry::number::ccw {

  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

}
#line 2 "src/real-geometry/operation/cross-product.hpp"

#line 4 "src/real-geometry/operation/cross-product.hpp"

namespace geometry {

  template< typename R >
  R cross_product(const vec2d<R> &a, const vec2d<R> &b) {
    return a.x() * b.y() - a.y() * b.x();
  }

}
#line 8 "src/real-geometry/operation/ccw.hpp"

namespace geometry {

  using namespace geometry::number::ccw;

  template< typename R >
  int ccw(const point<R> &a, point<R> b, point<R> c) {
    b = b - a, c = c - a;
    if (sign(cross_product(b, c)) == +1) return COUNTER_CLOCKWISE;
    if (sign(cross_product(b, c)) == -1) return CLOCKWISE;
    if (sign(inner_product(b, c)) == -1) return ONLINE_BACK;
    if (std::norm(b) < std::norm(c)) return ONLINE_FRONT;
    return ON_SEGMENT;
  }
}
#line 7 "src/real-geometry/distance/distance-sp.hpp"

#line 9 "src/real-geometry/distance/distance-sp.hpp"
#include <algorithm>

namespace geometry {

  template< typename R >
  R distance_sp(const segment<R> &s, const point<R> &p) {
    point<R> pr = projection({s.a, s.b}, p);
    if (ccw(s.a, s.b, pr) == 0) return std::abs(pr - p);
    return std::min(std::abs(s.a - p), std::abs(s.b - p));
  }

}
#line 2 "src/real-geometry/utility/polygon-to-segments.hpp"

#line 2 "src/real-geometry/utility/next-idx.hpp"

#line 4 "src/real-geometry/utility/next-idx.hpp"

namespace geometry {

  inline usize next_idx(usize idx, usize size) {
    return idx + 1 == size ? 0 : idx + 1;
  }

}
#line 7 "src/real-geometry/utility/polygon-to-segments.hpp"

namespace geometry {

  template< typename R >
  segments<R> polygon_to_segments(const polygon<R> &poly) {
    usize n = poly.size();

    segments<R> segs(n);
    for (usize i = 0; i < n; i++) {
      segs[i] = segment<R>(poly[i], poly[next_idx(i, n)]);
    }

    return segs;
  }

}
#line 14 "src/real-geometry/area/common-area-circle-polygon.hpp"

#line 18 "src/real-geometry/area/common-area-circle-polygon.hpp"

namespace geometry::internal {

  template< typename R >
  R impl_common_area_ca_cp(const circle<R> &c, const segment<R> &s) {
    point<R> va = c.o - s.a, vb = c.o - s.b;
    R f = cross_product(va, vb), res = 0;

    if (sign(f) == 0) return res;
    if (sign(std::max(std::abs(va), std::abs(vb)) - c.r) <= 0) return f;

    point<R> d(inner_product(va, vb), cross_product(va, vb));
    if (sign(distance_sp(s, c.o) - c.r) >= 0) {
      return std::norm(c.r) * std::atan2(d.y(), d.x());
    }

    points<R> ps = cross_point_cl(c, {s.a, s.b});
    if (ps.empty()) return res;
    if (ps.size() == 2 and sign(inner_product<R>(ps[1] - ps[0], s.a - ps[0])) >= 0) {
      std::swap(ps[0], ps[1]);
    }

    ps.emplace(ps.begin(), s.a);
    ps.emplace_back(s.b);
    for (usize i = 1; i < ps.size(); i++) {
      if (equals(ps[i - 1], ps[i])) continue;
      res += impl_common_area_ca_cp(c, {ps[i - 1], ps[i]});
    }

    return res;
  }

}

namespace geometry {

  template< typename R >
  R common_area_circle_polygon(const circle<R> &c, const polygon<R> &p) {
    usize n = p.size();
    if (n < 3) return 0;

    auto segs = polygon_to_segments(p);

    R res = 0;
    for (auto &seg: segs) {
      res += internal::impl_common_area_ca_cp(c, seg);
    }
    
    return res / 2;
  }

}
#line 2 "src/real-geometry/utility/io-set.hpp"

#include <iomanip>

namespace geometry {

  class IoSetup {
    using u32 = unsigned int;

    void set(std::ostream &os, u32 precision) {
      os << std::fixed << std::setprecision(precision);
    }

   public:
    IoSetup(u32 precision = 15) {
      std::cin.tie(0);
      std::ios::sync_with_stdio(0);

      set(std::cout, precision);
      set(std::cerr, precision);
    }
  } iosetup;

}
#line 9 "test/aoj/cgl/7_H.test.cpp"

#line 11 "test/aoj/cgl/7_H.test.cpp"

int main() {
  using R = long double;

  int n;
  R r;
  std::cin >> n >> r;

  geometry::circle<R> c({0, 0}, r);

  geometry::polygon<R> poly(n);
  for (auto &p : poly) std::cin >> p;

  std::cout << geometry::common_area_circle_polygon(c, poly) << std::endl;
}
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