geometry/cross_point_cc.hpp

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• Last update: 2026-08-10 07:05:08+00:00
• Include: #include "geometry/cross_point_cc.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E

Depends on

• geometry/base.hpp
• geometry/circle.hpp
• geometry/point.hpp

Verified with

• test/verify/aoj-cgl-7-e.test.cpp

Code

#pragma once

#include <cmath>

#include "base.hpp"
#include "circle.hpp"
#include "point.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 = std::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 = std::acos((std::norm(c1.r) - std::norm(c2.r) + std::norm(d)) /
                     (2 * c1.r * d));
  Real t = std::arg(c2.p - c1.p);
  Point p = c1.p + std::polar(c1.r, t + a);
  Point q = c1.p + std::polar(c1.r, t - a);
  if (equals(std::real(p), std::real(q)) && equals(std::imag(p), std::imag(q)))
    return {p};
  return {p, q};
}
}  // namespace geometry

#line 2 "geometry/cross_point_cc.hpp"

#include <cmath>

#line 2 "geometry/base.hpp"

#line 4 "geometry/base.hpp"

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = std::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; }
}  // namespace geometry
#line 2 "geometry/circle.hpp"

#include <vector>

#line 2 "geometry/point.hpp"

#line 4 "geometry/point.hpp"
#include <complex>
#include <iostream>
#line 7 "geometry/point.hpp"

#line 9 "geometry/point.hpp"

namespace geometry {
using Point = std::complex<Real>;

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

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

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

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

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

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

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

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

using Points = std::vector<Point>;
}  // namespace geometry
#line 6 "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 = std::vector<Circle>;
}  // namespace geometry
#line 8 "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 = std::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 = std::acos((std::norm(c1.r) - std::norm(c2.r) + std::norm(d)) /
                     (2 * c1.r * d));
  Real t = std::arg(c2.p - c1.p);
  Point p = c1.p + std::polar(c1.r, t + a);
  Point q = c1.p + std::polar(c1.r, t - a);
  if (equals(std::real(p), std::real(q)) && equals(std::imag(p), std::imag(q)))
    return {p};
  return {p, q};
}
}  // namespace geometry

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