Luzhiled's Library

This documentation is automatically generated by competitive-verifier/competitive-verifier

View the Project on GitHub ei1333/library

:heavy_check_mark: geometry/common_area_cp.hpp

Depends on

Verified with

Code

#pragma once

#include <algorithm>
#include <complex>

#include "base.hpp"
#include "cross_point_cl.hpp"
#include "distance_sp.hpp"
#include "is_intersect_cs.hpp"
#include "point.hpp"
#include "polygon.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(std::max(std::abs(va), std::abs(vb)) - c.r) <= 0) return f;
  if (sign(distance_sp(Segment(a, b), c.p) - c.r) >= 0)
    return std::norm(c.r) * std::arg(vb * std::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) {
    std::swap(tot[0], tot[1]);
  }
  tot.emplace(tot.begin(), 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;
}
}  // namespace geometry

#line 2 "geometry/common_area_cp.hpp"

#include <algorithm>
#include <complex>

#line 2 "geometry/base.hpp"

#include <cmath>

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = std::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 2 "geometry/cross_point_cl.hpp"

#line 4 "geometry/cross_point_cl.hpp"

#line 2 "geometry/circle.hpp"

#include <vector>

#line 2 "geometry/point.hpp"

#line 5 "geometry/point.hpp"
#include <iostream>
#line 7 "geometry/point.hpp"

#line 9 "geometry/point.hpp"

namespace geometry {
using Point = std::complex<Real>;

std::istream& operator>>(std::istream& is, Point& p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

std::ostream& operator<<(std::ostream& os, const Point& p) {
  return os << std::real(p) << " " << std::imag(p);
}

Point operator*(const Point& p, const Real& d) {
  return Point(std::real(p) * d, std::imag(p) * d);
}

// rotate point p counterclockwise by theta rad
Point rotate(Real theta, const Point& p) {
  return Point(std::cos(theta) * std::real(p) - std::sin(theta) * std::imag(p),
               std::sin(theta) * std::real(p) + std::cos(theta) * std::imag(p));
}

Real cross(const Point& a, const Point& b) {
  return std::real(a) * std::imag(b) - std::imag(a) * std::real(b);
}

Real dot(const Point& a, const Point& b) {
  return std::real(a) * std::real(b) + std::imag(a) * std::imag(b);
}

bool compare_x(const Point& a, const Point& b) {
  return equals(std::real(a), std::real(b)) ? std::imag(a) < std::imag(b)
                                            : std::real(a) < std::real(b);
}

bool compare_y(const Point& a, const Point& b) {
  return equals(std::imag(a), std::imag(b)) ? std::real(a) < std::real(b)
                                            : std::imag(a) < std::imag(b);
}

using Points = std::vector<Point>;
}  // namespace geometry
#line 6 "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 = std::vector<Circle>;
}  // namespace geometry
#line 2 "geometry/line.hpp"

#include <cassert>
#line 6 "geometry/line.hpp"

#line 8 "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 if (equals(C, 0)) {
      a = Point(0, C / B);
      b = Point(1, (C - A) / B);
    } else {
      a = Point(0, C / B);
      b = Point(C / A, 0);
    }
  }

  friend std::ostream& operator<<(std::ostream& os, Line& l) {
    return os << l.a << " to " << l.b;
  }

  friend std::istream& operator>>(std::istream& is, Line& l) {
    return is >> l.a >> l.b;
  }
};

using Lines = std::vector<Line>;
}  // namespace geometry
#line 2 "geometry/projection.hpp"

#line 4 "geometry/projection.hpp"

#line 7 "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) / std::norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
}  // namespace geometry
#line 10 "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(std::abs(pr - c.p), c.r)) return {pr};
  Point e = (l.b - l.a) / std::abs(l.b - l.a);
  auto k = std::sqrt(std::norm(c.r) - std::norm(pr - c.p));
  return {pr - e * k, pr + e * k};
}
}  // namespace geometry
#line 2 "geometry/distance_sp.hpp"

#line 4 "geometry/distance_sp.hpp"

#line 2 "geometry/is_intersect_sp.hpp"

#line 2 "geometry/ccw.hpp"

#line 4 "geometry/ccw.hpp"

#line 6 "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 (std::norm(b) < std::norm(c)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
}  // namespace geometry
#line 2 "geometry/segment.hpp"

#line 4 "geometry/segment.hpp"

#line 6 "geometry/segment.hpp"

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

  using Line::Line;
};

using Segments = std::vector<Segment>;
}  // namespace geometry
#line 6 "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 9 "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 std::abs(r - p);
  return std::min(std::abs(s.a - p), std::abs(s.b - p));
}
}  // namespace geometry
#line 2 "geometry/is_intersect_cs.hpp"

#line 4 "geometry/is_intersect_cs.hpp"

#line 10 "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(std::norm(h - c.p) - std::norm(c.r)) > 0) return 0;
  auto d1 = std::abs(c.p - l.a), d2 = std::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;
}
}  // namespace geometry
#line 2 "geometry/polygon.hpp"

#line 4 "geometry/polygon.hpp"

#line 6 "geometry/polygon.hpp"

namespace geometry {
using Polygon = std::vector<Point>;
using Polygons = std::vector<Polygon>;
}  // namespace geometry
#line 12 "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(std::max(std::abs(va), std::abs(vb)) - c.r) <= 0) return f;
  if (sign(distance_sp(Segment(a, b), c.p) - c.r) >= 0)
    return std::norm(c.r) * std::arg(vb * std::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) {
    std::swap(tot[0], tot[1]);
  }
  tot.emplace(tot.begin(), 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;
}
}  // namespace geometry
Back to top page