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View the Project on GitHub Luzhiled/comp-geometry
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_F // verification-helper: ERROR 0.00001 #include "src/real-geometry/circle-lib/tangent-cp.hpp" #include "src/real-geometry/class/circle.hpp" #include "src/real-geometry/class/point.hpp" #include "src/real-geometry/compare/compare-x.hpp" #include "src/real-geometry/utility/io-set.hpp" #include <iostream> #include <algorithm> int main() { using R = long double; geometry::point<R> p; std::cin >> p; geometry::circle<R> c; std::cin >> c.o >> c.r; geometry::points<R> pts = geometry::tangent_cp(c, p); std::sort(pts.begin(), pts.end(), geometry::compare_x<R>); for (auto &p : pts) std::cout << p.x() << " " << p.y() << std::endl; }
#line 1 "test/aoj/cgl/7_F.test.cpp" // verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_F // verification-helper: ERROR 0.00001 #line 2 "src/real-geometry/circle-lib/tangent-cp.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/cross-point/cross-point-cc.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 7 "src/real-geometry/cross-point/cross-point-cc.hpp" #line 9 "src/real-geometry/cross-point/cross-point-cc.hpp" #include <cmath> namespace geometry { template< typename R > points<R> cross_point_cc(const circle<R> &a, const circle<R> &b) { R d = std::abs(a.o - b.o), r = a.r + b.r; if (sign(d - r) > 0 or sign(d + a.r - b.r) < 0) return {}; R s = std::acos( (std::norm(a.r) - std::norm(b.r) + std::norm(d)) / (2 * a.r * d) ); R t = std::arg(b.o - a.o); point<R> p{a.o + std::polar(a.r, t + s)}; point<R> q{a.o + std::polar(a.r, t - s)}; if (equals(p, q)) return {p}; return {p, q}; } } #line 6 "src/real-geometry/circle-lib/tangent-cp.hpp" #line 9 "src/real-geometry/circle-lib/tangent-cp.hpp" namespace geometry { template< typename R > points<R> tangent_cp(const circle<R> &c, const point<R> &p) { circle<R> t{p, std::sqrt(std::norm(c.o - p) - std::norm(c.r))}; return cross_point_cc(c, t); } } #line 2 "src/real-geometry/compare/compare-x.hpp" #line 5 "src/real-geometry/compare/compare-x.hpp" namespace geometry { template< typename R > bool compare_x(const point<R> &a, const point<R> &b) { return not equals(a.x(), b.x()) ? a.x() < b.x() : a.y() < b.y(); } } #line 2 "src/real-geometry/utility/io-set.hpp" #include <iomanip> namespace geometry { class IoSetup { using u32 = unsigned int; void set(std::ostream &os, u32 precision) { os << std::fixed << std::setprecision(precision); } public: IoSetup(u32 precision = 15) { std::cin.tie(0); std::ios::sync_with_stdio(0); set(std::cout, precision); set(std::cerr, precision); } } iosetup; } #line 9 "test/aoj/cgl/7_F.test.cpp" #line 11 "test/aoj/cgl/7_F.test.cpp" #include <algorithm> int main() { using R = long double; geometry::point<R> p; std::cin >> p; geometry::circle<R> c; std::cin >> c.o >> c.r; geometry::points<R> pts = geometry::tangent_cp(c, p); std::sort(pts.begin(), pts.end(), geometry::compare_x<R>); for (auto &p : pts) std::cout << p.x() << " " << p.y() << std::endl; }