src/real-geometry/area/polygon-area.hpp

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Last update: 2023-05-30 15:21:05+09:00
Include: #include "src/real-geometry/area/polygon-area.hpp"

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#pragma once

#include "src/real-geometry/common/size-alias.hpp"
#include "src/real-geometry/class/polygon.hpp"
#include "src/real-geometry/operation/cross-product.hpp"
#include "src/real-geometry/utility/next-idx.hpp"

namespace geometry {

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

    R res = 0;
    for (usize i = 0; i < n; ++i) {
      res += cross_product(poly[i], poly[next_idx(i, n)]);
    }
    return res / 2;
  }

}

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

#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/class/polygon.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/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/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 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/area/polygon-area.hpp"

namespace geometry {

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

    R res = 0;
    for (usize i = 0; i < n; ++i) {
      res += cross_product(poly[i], poly[next_idx(i, n)]);
    }
    return res / 2;
  }

}