Luzhiled's Library

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:heavy_check_mark: geometry/area.hpp

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Code

#pragma once

#include "point.hpp"
#include "polygon.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
Real area(const Polygon& p) {
  int n = (int)p.size();
  Real A = 0;
  for (int i = 0; i < n; ++i) {
    A += cross(p[i], p[(i + 1) % n]);
  }
  return A * 0.5;
}
}  // namespace geometry

#line 2 "geometry/area.hpp"

#line 2 "geometry/point.hpp"

#include <cmath>
#include <complex>
#include <iostream>
#include <vector>

#line 2 "geometry/base.hpp"

#line 4 "geometry/base.hpp"

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 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 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 5 "geometry/area.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
Real area(const Polygon& p) {
  int n = (int)p.size();
  Real A = 0;
  for (int i = 0; i < n; ++i) {
    A += cross(p[i], p[(i + 1) % n]);
  }
  return A * 0.5;
}
}  // namespace geometry
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