comp-geometry

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:heavy_check_mark: src/real-geometry/circle-lib/tangent-cc.hpp

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Code

#pragma once

#include "src/real-geometry/class/circle.hpp"
#include "src/real-geometry/class/line.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/utility/sign.hpp"

#include <algorithm>
#include <cmath>
#include <complex>

namespace geometry {

  template< typename R >
  lines<R> tangent_cc(circle<R> a, circle<R> b) {
    lines<R> ls;
    if (a.r > b.r) std::swap(a, b);

    auto d = a.o - b.o;
    R g = norm(d);

    if (sign(g) == 0) return ls;

    point<R> u = d / std::sqrt(g);
    point<R> v(-u.y(), u.x());

    for (int s = 1; s >= -1; s -= 2) {
      R h = (a.r * s + b.r) / std::sqrt(g);

      auto dh = 1 - std::norm(h);
      if (sign(dh) == 0) {
        ls.emplace_back(b.o + u * b.r, b.o + (u + v) * b.r);
      }
      
      else if (sign(dh) > 0) {
        auto uu = u * h;
        auto vv = v * std::sqrt(dh);
        ls.emplace_back(b.o + (uu + vv) * b.r, a.o - (uu + vv) * a.r * (R)s);
        ls.emplace_back(b.o + (uu - vv) * b.r, a.o - (uu - vv) * a.r * (R)s);
      }
    }

    return ls;
  }

}
#line 2 "src/real-geometry/circle-lib/tangent-cc.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/class/line.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 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 7 "src/real-geometry/circle-lib/tangent-cc.hpp"

#include <algorithm>
#include <cmath>
#line 11 "src/real-geometry/circle-lib/tangent-cc.hpp"

namespace geometry {

  template< typename R >
  lines<R> tangent_cc(circle<R> a, circle<R> b) {
    lines<R> ls;
    if (a.r > b.r) std::swap(a, b);

    auto d = a.o - b.o;
    R g = norm(d);

    if (sign(g) == 0) return ls;

    point<R> u = d / std::sqrt(g);
    point<R> v(-u.y(), u.x());

    for (int s = 1; s >= -1; s -= 2) {
      R h = (a.r * s + b.r) / std::sqrt(g);

      auto dh = 1 - std::norm(h);
      if (sign(dh) == 0) {
        ls.emplace_back(b.o + u * b.r, b.o + (u + v) * b.r);
      }
      
      else if (sign(dh) > 0) {
        auto uu = u * h;
        auto vv = v * std::sqrt(dh);
        ls.emplace_back(b.o + (uu + vv) * b.r, a.o - (uu + vv) * a.r * (R)s);
        ls.emplace_back(b.o + (uu - vv) * b.r, a.o - (uu - vv) * a.r * (R)s);
      }
    }

    return ls;
  }

}
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