src/real-geometry/convex/is-convex.hpp

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Last update: 2023-05-31 11:05:34+09:00
Include: #include "src/real-geometry/convex/is-convex.hpp"

Depends on

Verified with

test/aoj/cgl/3_B.test.cpp

Code

#pragma once

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

namespace geometry {

  template< typename R >
  bool is_convex(const polygon<R> &poly) {
    usize n = poly.size();
    for (usize i = 0; i < n; i++) {
      if (ccw(poly[prev_idx(i, n)], poly[i], poly[next_idx(i, n)]) != -1) continue;
      return false;
    }
    return true;
  }

}

#line 2 "src/real-geometry/convex/is-convex.hpp"

#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/common/size-alias.hpp"

#include <cstddef>

namespace geometry {

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

}
#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 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 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 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 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 2 "src/real-geometry/utility/prev-idx.hpp"

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

namespace geometry {

  inline usize prev_idx(usize idx, usize size) {
    return idx ? idx - 1 : size - 1;
  }

}
#line 8 "src/real-geometry/convex/is-convex.hpp"

namespace geometry {

  template< typename R >
  bool is_convex(const polygon<R> &poly) {
    usize n = poly.size();
    for (usize i = 0; i < n; i++) {
      if (ccw(poly[prev_idx(i, n)], poly[i], poly[next_idx(i, n)]) != -1) continue;
      return false;
    }
    return true;
  }

}