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View the Project on GitHub Luzhiled/comp-geometry
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_G // verification-helper: ERROR 0.00001 #include "src/real-geometry/circle-lib/tangent-cc.hpp" #include "src/real-geometry/class/circle.hpp" #include "src/real-geometry/class/line.hpp" #include "src/real-geometry/class/point.hpp" #include "src/real-geometry/compare/compare-x.hpp" #include "src/real-geometry/mapping/projection.hpp" #include "src/real-geometry/utility/io-set.hpp" #include <iostream> #include <algorithm> using namespace geometry; int main() { using R = long double; geometry::circle<R> c1, c2; std::cin >> c1.o >> c1.r; std::cin >> c2.o >> c2.r; geometry::lines<R> ls = geometry::tangent_cc(c1, c2); geometry::points<R> ps; for (auto &l : ls) ps.emplace_back(geometry::projection(l, c1.o)); std::sort(ps.begin(), ps.end(), geometry::compare_x<R>); for (auto &p : ps) std::cout << p.x() << " " << p.y() << std::endl; }
#line 1 "test/aoj/cgl/7_G.test.cpp" // verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/CGL_7_G // verification-helper: ERROR 0.00001 #line 2 "src/real-geometry/circle-lib/tangent-cc.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/class/line.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 5 "src/real-geometry/class/line.hpp" #include <cassert> #line 8 "src/real-geometry/class/line.hpp" namespace geometry { template< typename R > class line { using P = point<R>; public: P a, b; line() = default; line(P a, P b) : a(a), b(b) { assert(not equals(a, b)); } }; template< typename R > using lines = std::vector< line<R> >; } #line 7 "src/real-geometry/circle-lib/tangent-cc.hpp" #include <algorithm> #include <cmath> #line 11 "src/real-geometry/circle-lib/tangent-cc.hpp" namespace geometry { template< typename R > lines<R> tangent_cc(circle<R> a, circle<R> b) { lines<R> ls; if (a.r > b.r) std::swap(a, b); auto d = a.o - b.o; R g = norm(d); if (sign(g) == 0) return ls; point<R> u = d / std::sqrt(g); point<R> v(-u.y(), u.x()); for (int s = 1; s >= -1; s -= 2) { R h = (a.r * s + b.r) / std::sqrt(g); auto dh = 1 - std::norm(h); if (sign(dh) == 0) { ls.emplace_back(b.o + u * b.r, b.o + (u + v) * b.r); } else if (sign(dh) > 0) { auto uu = u * h; auto vv = v * std::sqrt(dh); ls.emplace_back(b.o + (uu + vv) * b.r, a.o - (uu + vv) * a.r * (R)s); ls.emplace_back(b.o + (uu - vv) * b.r, a.o - (uu - vv) * a.r * (R)s); } } return ls; } } #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/mapping/projection.hpp" #line 2 "src/real-geometry/operation/inner-product.hpp" #line 4 "src/real-geometry/operation/inner-product.hpp" namespace geometry { template< typename R > R inner_product(const vec2d<R> &a, const vec2d<R> &b) { return a.x() * b.x() + a.y() * b.y(); } } #line 6 "src/real-geometry/mapping/projection.hpp" #line 8 "src/real-geometry/mapping/projection.hpp" namespace geometry { template< typename R > point<R> projection(const line<R> &l, const point<R> &p) { R t = inner_product<R>(p - l.a, l.a - l.b) / std::norm(l.a - l.b); return l.a + (l.a - l.b) * t; } } #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 11 "test/aoj/cgl/7_G.test.cpp" #line 14 "test/aoj/cgl/7_G.test.cpp" using namespace geometry; int main() { using R = long double; geometry::circle<R> c1, c2; std::cin >> c1.o >> c1.r; std::cin >> c2.o >> c2.r; geometry::lines<R> ls = geometry::tangent_cc(c1, c2); geometry::points<R> ps; for (auto &l : ls) ps.emplace_back(geometry::projection(l, c1.o)); std::sort(ps.begin(), ps.end(), geometry::compare_x<R>); for (auto &p : ps) std::cout << p.x() << " " << p.y() << std::endl; }