src/real-geometry/distance/distance-lp.hpp

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Last update: 2023-06-05 11:34:11+09:00
Include: #include "src/real-geometry/distance/distance-lp.hpp"

Depends on

Verified with

test/atcoder/abc181_f.test.cpp

Code

#pragma once

#include "src/real-geometry/class/line.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/mapping/projection.hpp"

namespace geometry {

  template< typename R >
  R distance_lp(const line<R> &l, const point<R> &p) {
    point<R> pr = projection(l, p);
    return std::abs(pr - p);
  }

}

#line 2 "src/real-geometry/distance/distance-lp.hpp"

#line 2 "src/real-geometry/class/line.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 2 "src/real-geometry/utility/equals/vector.hpp"

#line 2 "src/real-geometry/utility/equals/real-number.hpp"

#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 4 "src/real-geometry/utility/equals/real-number.hpp"

namespace geometry {

  template< typename R >
  bool equals(R a, R b) {
    return sign(a - b) == 0;
  }

}
#line 5 "src/real-geometry/utility/equals/vector.hpp"

namespace geometry {

  template< typename R >
  bool equals(const vec2d<R> &a, const vec2d<R> &b) {
    return equals(a.x(), b.x()) and equals(a.y(), b.y());
  }

}
#line 5 "src/real-geometry/class/line.hpp"

#include <cassert>
#line 8 "src/real-geometry/class/line.hpp"

namespace geometry {

  template< typename R >
  class line {
    using P = point<R>;

   public:
    P a, b;

    line() = default;
    line(P a, P b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using lines = std::vector< line<R> >;

}
#line 2 "src/real-geometry/mapping/projection.hpp"

#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 6 "src/real-geometry/mapping/projection.hpp"

#line 8 "src/real-geometry/mapping/projection.hpp"

namespace geometry {

  template< typename R >
  point<R> projection(const line<R> &l, const point<R> &p) {
    R t = inner_product<R>(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
    return l.a + (l.a - l.b) * t;
  }

}
#line 6 "src/real-geometry/distance/distance-lp.hpp"

namespace geometry {

  template< typename R >
  R distance_lp(const line<R> &l, const point<R> &p) {
    point<R> pr = projection(l, p);
    return std::abs(pr - p);
  }

}