src/real-geometry/circle-lib/tangent-cp.hpp

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Last update: 2023-06-01 02:20:58+09:00
Include: #include "src/real-geometry/circle-lib/tangent-cp.hpp"

Depends on

Verified with

test/aoj/cgl/7_F.test.cpp

Code

#pragma once

#include "src/real-geometry/class/circle.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/cross-point/cross-point-cc.hpp"

#include <complex>
#include <cmath>

namespace geometry {

  template< typename R >
  points<R> tangent_cp(const circle<R> &c, const point<R> &p) {
    circle<R> t{p, std::sqrt(std::norm(c.o - p) - std::norm(c.r))};

    return cross_point_cc(c, t);
  }

}

#line 2 "src/real-geometry/circle-lib/tangent-cp.hpp"

#line 2 "src/real-geometry/class/circle.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/circle.hpp"

#line 6 "src/real-geometry/class/circle.hpp"

// circle
namespace geometry {

  template< typename R >
  class circle {
   public:
    point<R> o;
    R r;

    circle() = default;
    circle(point<R> o, R r) : o(o), r(r) {}

    const point<R> center() const {
      return o;
    }

    const R radius() const {
      return r;
    }
  };


  template< typename R >
  using circles = std::vector< circle<R> >;

}
#line 2 "src/real-geometry/cross-point/cross-point-cc.hpp"

#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 7 "src/real-geometry/cross-point/cross-point-cc.hpp"

#line 9 "src/real-geometry/cross-point/cross-point-cc.hpp"
#include <cmath>

namespace geometry {

  template< typename R >
  points<R> cross_point_cc(const circle<R> &a, const circle<R> &b) {
    R d = std::abs(a.o - b.o), r = a.r + b.r;

    if (sign(d - r) > 0 or sign(d + a.r - b.r) < 0) return {};
    
    R s = std::acos( (std::norm(a.r) - std::norm(b.r) + std::norm(d)) / (2 * a.r * d) );
    R t = std::arg(b.o - a.o);

    point<R> p{a.o + std::polar(a.r, t + s)};
    point<R> q{a.o + std::polar(a.r, t - s)};

    if (equals(p, q)) return {p};
    return {p, q};
  }

}


#line 6 "src/real-geometry/circle-lib/tangent-cp.hpp"

#line 9 "src/real-geometry/circle-lib/tangent-cp.hpp"

namespace geometry {

  template< typename R >
  points<R> tangent_cp(const circle<R> &c, const point<R> &p) {
    circle<R> t{p, std::sqrt(std::norm(c.o - p) - std::norm(c.r))};

    return cross_point_cc(c, t);
  }

}