Luzhiled's Library

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:heavy_check_mark: geometry/cross_point_cl.hpp

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Code

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

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
Points cross_point_cl(const Circle &c, const Line &l) {
  Point pr = projection(l, c.p);
  if (equals(abs(pr - c.p), c.r)) return {pr};
  Point e = (l.b - l.a) / abs(l.b - l.a);
  auto k = sqrt(norm(c.r) - norm(pr - c.p));
  return {pr - e * k, pr + e * k};
}
}  // namespace geometry

#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; }
}  // namespace geometry
#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>;
}  // namespace geometry
#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>;
}  // namespace geometry
#line 3 "geometry/line.hpp"

namespace geometry {
struct Line {
  Point a, b;

  Line() = default;

  Line(const Point &a, const Point &b) : a(a), b(b) {}

  Line(const Real &A, const Real &B, const Real &C) {  // Ax+By=C
    if (equals(A, 0)) {
      assert(!equals(B, 0));
      a = Point(0, C / B);
      b = Point(1, C / B);
    } else if (equals(B, 0)) {
      a = Point(C / A, 0);
      b = Point(C / A, 1);
    } else {
      a = Point(0, C / B);
      b = Point(C / A, 0);
    }
  }

  friend ostream &operator<<(ostream &os, Line &l) {
    return os << l.a << " to " << l.b;
  }

  friend istream &operator>>(istream &is, Line &l) { return is >> l.a >> l.b; }
};

using Lines = vector<Line>;
}  // namespace geometry
#line 2 "geometry/projection.hpp"

#line 5 "geometry/projection.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
Point projection(const Line &l, const Point &p) {
  auto t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
}  // namespace geometry
#line 6 "geometry/cross_point_cl.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
Points cross_point_cl(const Circle &c, const Line &l) {
  Point pr = projection(l, c.p);
  if (equals(abs(pr - c.p), c.r)) return {pr};
  Point e = (l.b - l.a) / abs(l.b - l.a);
  auto k = sqrt(norm(c.r) - norm(pr - c.p));
  return {pr - e * k, pr + e * k};
}
}  // namespace geometry
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