Area of intersection between two circles
(Mylib/Geometry/Float/area_intersection_of_circles.cpp)

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Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

Educational Codeforces Round 2 D. Area of Two Circles’ Intersection

References

Depends on

Verified with

test/aoj/CGL_7_I/main.test.cpp

Code

#pragma once
#include "Mylib/Geometry/Float/geometry_template.cpp"
#include "Mylib/Geometry/Float/intersect_circles.cpp"

namespace haar_lib {
  template <typename T>
  T area_of_intersection_of_circles(const circle<T> &a, const circle<T> &b) {
    const auto s = intersect_circles(a, b);
    auto p       = s.crosspoints;

    if (s.is_same()) {
      return a.radius * a.radius * M_PI;
    } else if (s.is_inside() or s.is_inscribed()) {
      return std::min(a.radius * a.radius * M_PI, b.radius * b.radius * M_PI);
    } else if (s.is_intersected()) {
      T ret  = 0;
      auto d = abs(a.center - b.center);

      {
        T ang = acos((a.radius * a.radius + d * d - b.radius * b.radius) / (a.radius * d * 2.0));
        ret += (ang - sin(ang * 2.0) / 2.0) * a.radius * a.radius;
      }

      {
        T ang = acos((b.radius * b.radius + d * d - a.radius * a.radius) / (b.radius * d * 2.0));
        ret += (ang - sin(ang * 2.0) / 2.0) * b.radius * b.radius;
      }

      return ret;
    }

    return 0;
  }
}  // namespace haar_lib

#line 2 "Mylib/Geometry/Float/geometry_template.cpp"
#include <cmath>
#include <iostream>
#include <vector>

namespace haar_lib {
  template <typename T>
  struct vec {
    T x, y;
    vec() {}
    vec(T x, T y) : x(x), y(y) {}

    friend auto operator+(const vec &a, const vec &b) { return vec(a.x + b.x, a.y + b.y); }
    friend auto operator-(const vec &a, const vec &b) { return vec(a.x - b.x, a.y - b.y); }
    friend auto operator-(const vec &a) { return vec(-a.x, -a.y); }

    friend bool operator==(const vec &a, const vec &b) { return a.x == b.x and a.y == b.y; }
    friend bool operator!=(const vec &a, const vec &b) { return !(a == b); }
    friend bool operator<(const vec &a, const vec &b) { return a.x < b.x or (a.x == b.x and a.y < b.y); }

    friend std::istream &operator>>(std::istream &s, vec &a) {
      s >> a.x >> a.y;
      return s;
    }
  };

  template <typename T, typename U>
  auto operator*(const vec<T> &a, const U &k) { return vec<T>(a.x * k, a.y * k); }
  template <typename T, typename U>
  auto operator*(const U &k, const vec<T> &a) { return vec<T>(a.x * k, a.y * k); }
  template <typename T, typename U>
  auto operator/(const vec<T> &a, const U &k) { return vec<T>(a.x / k, a.y / k); }

  template <typename T>
  using point = vec<T>;

  template <typename T>
  T abs(const vec<T> &a) { return sqrt(a.x * a.x + a.y * a.y); }
  template <typename T>
  T abs_sq(const vec<T> &a) { return a.x * a.x + a.y * a.y; }

  template <typename T>
  T dot(const vec<T> &a, const vec<T> &b) { return a.x * b.x + a.y * b.y; }
  template <typename T>
  T cross(const vec<T> &a, const vec<T> &b) { return a.x * b.y - a.y * b.x; }

  template <typename T>
  auto unit(const vec<T> &a) { return a / abs(a); }
  template <typename T>
  auto normal(const vec<T> &p) { return vec<T>(-p.y, p.x); }

  template <typename T>
  auto polar(const T &r, const T &ang) { return vec<T>(r * cos(ang), r * sin(ang)); }

  template <typename T>
  T angle(const vec<T> &a, const vec<T> &b) { return atan2(b.y - a.y, b.x - a.x); }
  template <typename T>
  T phase(const vec<T> &a) { return atan2(a.y, a.x); }

  template <typename T>
  T angle_diff(const vec<T> &a, const vec<T> &b) {
    T r = phase(b) - phase(a);

    if (r < -M_PI)
      return r + 2 * M_PI;
    else if (r > M_PI)
      return r - 2 * M_PI;
    return r;
  }

  template <typename T>
  struct line {
    point<T> from, to;
    line() : from(), to() {}
    line(const point<T> &from, const point<T> &to) : from(from), to(to) {}
  };

  template <typename T>
  using segment = line<T>;

  template <typename T>
  auto unit(const line<T> &a) { return unit(a.to - a.from); }
  template <typename T>
  auto normal(const line<T> &a) { return normal(a.to - a.from); }

  template <typename T>
  auto diff(const segment<T> &a) { return a.to - a.from; }

  template <typename T>
  T abs(const segment<T> &a) { return abs(diff(a)); }

  template <typename T>
  T dot(const line<T> &a, const line<T> &b) { return dot(diff(a), diff(b)); }
  template <typename T>
  T cross(const line<T> &a, const line<T> &b) { return cross(diff(a), diff(b)); }

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

  template <typename T>
  struct circle {
    point<T> center;
    T radius;
    circle() : center(), radius(0) {}
    circle(const point<T> &center, T radius) : center(center), radius(radius) {}
  };

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const vec<T> &a) {
    s << "(" << a.x << ", " << a.y << ")";
    return s;
  }

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const line<T> &a) {
    s << "(" << a.from << " -> " << a.to << ")";
    return s;
  }

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const circle<T> &a) {
    s << "("
      << "center: " << a.center << ", "
      << "radius: " << a.radius << ")";
    return s;
  }
}  // namespace haar_lib
#line 4 "Mylib/Geometry/Float/intersect_circles.cpp"

namespace haar_lib {
  namespace intersect_circles_impl {
    enum class status_t { SAME,
                          INSIDE,
                          INSCRIBED,
                          INTERSECTED,
                          CIRCUMSCRIBED,
                          OUTSIDE };
    template <typename T>
    struct result {
      status_t status;
      std::vector<point<T>> crosspoints;
      bool is_same() const { return status == status_t::SAME; }
      bool is_inside() const { return status == status_t::INSIDE; }
      bool is_inscribed() const { return status == status_t::INSCRIBED; }
      bool is_intersected() const { return status == status_t::INTERSECTED; }
      bool is_circumscribed() const { return status == status_t::CIRCUMSCRIBED; }
      bool is_outside() const { return status == status_t::OUTSIDE; }
    };
  }  // namespace intersect_circles_impl

  template <typename T>
  auto intersect_circles(const circle<T> &a, const circle<T> &b) {
    using namespace intersect_circles_impl;

    const T d = abs(a.center - b.center);
    const T x = acos((a.radius * a.radius + d * d - b.radius * b.radius) / ((T) 2.0 * d * a.radius));
    const T t = atan2(b.center.y - a.center.y, b.center.x - a.center.x);

    if (a.radius + b.radius == d) {
      return result<T>({status_t::CIRCUMSCRIBED, {a.center + polar(a.radius, t)}});
    } else if (abs(a.radius - b.radius) == d) {
      return result<T>({status_t::INSCRIBED, {a.center + polar(a.radius, t)}});
    } else if (a.radius + b.radius > d and d > abs(a.radius - b.radius)) {
      return result<T>(
          {status_t::INTERSECTED,
           {a.center + polar(a.radius, t + x), a.center + polar(a.radius, t - x)}});
    } else if (a.radius + b.radius < d) {
      return result<T>({status_t::OUTSIDE, {}});
    } else if (abs(a.radius - b.radius) > d) {
      return result<T>({status_t::INSIDE, {}});
    }

    return result<T>({status_t::SAME, {}});
  }
}  // namespace haar_lib
#line 4 "Mylib/Geometry/Float/area_intersection_of_circles.cpp"

namespace haar_lib {
  template <typename T>
  T area_of_intersection_of_circles(const circle<T> &a, const circle<T> &b) {
    const auto s = intersect_circles(a, b);
    auto p       = s.crosspoints;

    if (s.is_same()) {
      return a.radius * a.radius * M_PI;
    } else if (s.is_inside() or s.is_inscribed()) {
      return std::min(a.radius * a.radius * M_PI, b.radius * b.radius * M_PI);
    } else if (s.is_intersected()) {
      T ret  = 0;
      auto d = abs(a.center - b.center);

      {
        T ang = acos((a.radius * a.radius + d * d - b.radius * b.radius) / (a.radius * d * 2.0));
        ret += (ang - sin(ang * 2.0) / 2.0) * a.radius * a.radius;
      }

      {
        T ang = acos((b.radius * b.radius + d * d - a.radius * a.radius) / (b.radius * d * 2.0));
        ret += (ang - sin(ang * 2.0) / 2.0) * b.radius * b.radius;
      }

      return ret;
    }

    return 0;
  }
}  // namespace haar_lib

kyopro-lib

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

Area of intersection between two circles
(Mylib/Geometry/Float/area_intersection_of_circles.cpp)

Operations

Requirements

Notes

Problems

References

Depends on

Verified with

Code

Area of intersection between two circles (Mylib/Geometry/Float/area_intersection_of_circles.cpp)

Operations

Requirements

Notes

Problems

References

Depends on

Verified with

Code

Area of intersection between two circles
(Mylib/Geometry/Float/area_intersection_of_circles.cpp)