geometry/cross_point_cc.hpp

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Last update: 2022-09-11 00:53:50+09:00
Include: #include "geometry/cross_point_cc.hpp"
Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E

Depends on

Verified with

test/verify/aoj-cgl-7-e.test.cpp

Code

#include "base.hpp"
#include "point.hpp"
#include "circle.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E
  Points cross_point_cc(const Circle &c1, const Circle &c2) {
    Real d = abs(c1.p - c2.p), r = c1.r + c2.r;
    if(sign(d - r) > 0 or sign(d + c1.r - c2.r) < 0) return {};
    Real a = acos((norm(c1.r) - norm(c2.r) + norm(d)) / (2 * c1.r * d));
    Real t = arg(c2.p - c1.p);
    Point p = c1.p + polar(c1.r, t + a);
    Point q = c1.p + polar(c1.r, t - a);
    if(equals(real(p), real(q)) && equals(imag(p), imag(q))) return {p};
    return {p, q};
  }
}

#line 2 "geometry/base.hpp"

namespace geometry {
  using Real = double;
  const Real EPS = 1e-8;
  const Real PI = acos(static_cast< Real >(-1));

  enum {
    OUT, ON, IN
  };

  inline int sign(const Real &r) {
    return r <= -EPS ? -1 : r >= EPS ? 1 : 0;
  }

  inline bool equals(const Real &a, const Real &b) {
    return sign(a - b) == 0;
  }
}
#line 3 "geometry/point.hpp"

namespace geometry {
  using Point = complex< Real >;

  istream &operator>>(istream &is, Point &p) {
    Real a, b;
    is >> a >> b;
    p = Point(a, b);
    return is;
  }

  ostream &operator<<(ostream &os, const Point &p) {
    return os << real(p) << " " << imag(p);
  }

  Point operator*(const Point &p, const Real &d) {
    return Point(real(p) * d, imag(p) * d);
  }

  // rotate point p counterclockwise by theta rad
  Point rotate(Real theta, const Point &p) {
    return Point(cos(theta) * real(p) - sin(theta) * imag(p), sin(theta) * real(p) + cos(theta) * imag(p));
  }

  Real cross(const Point &a, const Point &b) {
    return real(a) * imag(b) - imag(a) * real(b);
  }

  Real dot(const Point &a, const Point &b) {
    return real(a) * real(b) + imag(a) * imag(b);
  }

  bool compare_x(const Point &a, const Point &b) {
    return equals(real(a), real(b)) ? imag(a) < imag(b) : real(a) < real(b);
  }

  bool compare_y(const Point &a, const Point &b) {
    return equals(imag(a), imag(b)) ? real(a) < real(b) : imag(a) < imag(b);
  }

  using Points = vector< Point >;
}
#line 3 "geometry/circle.hpp"

namespace geometry {
  struct Circle {
    Point p;
    Real r{};

    Circle() = default;

    Circle(const Point &p, const Real &r) : p(p), r(r) {}
  };

  using Circles = vector< Circle >;
}
#line 4 "geometry/cross_point_cc.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E
  Points cross_point_cc(const Circle &c1, const Circle &c2) {
    Real d = abs(c1.p - c2.p), r = c1.r + c2.r;
    if(sign(d - r) > 0 or sign(d + c1.r - c2.r) < 0) return {};
    Real a = acos((norm(c1.r) - norm(c2.r) + norm(d)) / (2 * c1.r * d));
    Real t = arg(c2.p - c1.p);
    Point p = c1.p + polar(c1.r, t + a);
    Point q = c1.p + polar(c1.r, t - a);
    if(equals(real(p), real(q)) && equals(imag(p), imag(q))) return {p};
    return {p, q};
  }
}