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#include "geometry/is_intersect_cs.hpp"
#include "base.hpp"
#include "point.hpp"
#include "segment.hpp"
#include "circle.hpp"
#include "projection.hpp"
namespace geometry {
int is_intersect_cs(const Circle &c, const Segment &l) {
Point h = projection(l, c.p);
if(sign(norm(h - c.p) - norm(c.r)) > 0) return 0;
auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
if(sign(c.r - d1) >= 0 && sign(c.r - d2) >= 0) return 0;
if(sign(c.r - d1) < 0 && sign(d2 - c.r) > 0 || sign(d1 - c.r) > 0 && sign(c.r - d2) < 0) return 1;
if(sign(dot(l.a - h, l.b - h)) < 0) return 2;
return 0;
}
}
#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/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 >;
}
#line 3 "geometry/segment.hpp"
namespace geometry {
struct Segment : Line {
Segment() = default;
using Line::Line;
};
using Segments = vector< Segment >;
}
#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 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;
}
}
#line 6 "geometry/is_intersect_cs.hpp"
namespace geometry {
int is_intersect_cs(const Circle &c, const Segment &l) {
Point h = projection(l, c.p);
if(sign(norm(h - c.p) - norm(c.r)) > 0) return 0;
auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
if(sign(c.r - d1) >= 0 && sign(c.r - d2) >= 0) return 0;
if(sign(c.r - d1) < 0 && sign(d2 - c.r) > 0 || sign(d1 - c.r) > 0 && sign(c.r - d2) < 0) return 1;
if(sign(dot(l.a - h, l.b - h)) < 0) return 2;
return 0;
}
}