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View the Project on GitHub Luzhiled/comp-geometry
#include "src/real-geometry/area/common-area-circle-polygon.hpp"
#pragma once #include "src/real-geometry/class/circle.hpp" #include "src/real-geometry/class/point.hpp" #include "src/real-geometry/class/polygon.hpp" #include "src/real-geometry/class/segment.hpp" #include "src/real-geometry/common/size-alias.hpp" #include "src/real-geometry/cross-point/cross-point-cl.hpp" #include "src/real-geometry/distance/distance-sp.hpp" #include "src/real-geometry/numbers/sign.hpp" #include "src/real-geometry/operation/cross-product.hpp" #include "src/real-geometry/operation/inner-product.hpp" #include "src/real-geometry/utility/polygon-to-segments.hpp" #include <algorithm> #include <complex> #include <cmath> namespace geometry::internal { template< typename R > R impl_common_area_ca_cp(const circle<R> &c, const segment<R> &s) { point<R> va = c.o - s.a, vb = c.o - s.b; R f = cross_product(va, vb), res = 0; if (sign(f) == 0) return res; if (sign(std::max(std::abs(va), std::abs(vb)) - c.r) <= 0) return f; point<R> d(inner_product(va, vb), cross_product(va, vb)); if (sign(distance_sp(s, c.o) - c.r) >= 0) { return std::norm(c.r) * std::atan2(d.y(), d.x()); } points<R> ps = cross_point_cl(c, {s.a, s.b}); if (ps.empty()) return res; if (ps.size() == 2 and sign(inner_product<R>(ps[1] - ps[0], s.a - ps[0])) >= 0) { std::swap(ps[0], ps[1]); } ps.emplace(ps.begin(), s.a); ps.emplace_back(s.b); for (usize i = 1; i < ps.size(); i++) { if (equals(ps[i - 1], ps[i])) continue; res += impl_common_area_ca_cp(c, {ps[i - 1], ps[i]}); } return res; } } namespace geometry { template< typename R > R common_area_circle_polygon(const circle<R> &c, const polygon<R> &p) { usize n = p.size(); if (n < 3) return 0; auto segs = polygon_to_segments(p); R res = 0; for (auto &seg: segs) { res += internal::impl_common_area_ca_cp(c, seg); } return res / 2; } }
#line 2 "src/real-geometry/area/common-area-circle-polygon.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/polygon.hpp" #line 4 "src/real-geometry/class/polygon.hpp" #line 6 "src/real-geometry/class/polygon.hpp" namespace geometry { template< typename R > using polygon = std::vector< point<R> >; template< typename R > using polygons = std::vector< polygon<R> >; } #line 2 "src/real-geometry/class/segment.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/segment.hpp" #include <cassert> #line 8 "src/real-geometry/class/segment.hpp" namespace geometry { template< typename R > class segment { public: point<R> a, b; segment() = default; segment(point<R> a, point<R> b) : a(a), b(b) { assert(not equals(a, b)); } }; template< typename R > using segments = std::vector< segment<R> >; } #line 2 "src/real-geometry/common/size-alias.hpp" #include <cstddef> namespace geometry { using isize = std::ptrdiff_t; using usize = std::size_t; } #line 2 "src/real-geometry/cross-point/cross-point-cl.hpp" #line 2 "src/real-geometry/class/line.hpp" #line 5 "src/real-geometry/class/line.hpp" #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 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 7 "src/real-geometry/cross-point/cross-point-cl.hpp" #include <cmath> #line 10 "src/real-geometry/cross-point/cross-point-cl.hpp" namespace geometry { template< typename R > points<R> cross_point_cl(const circle<R> &c, const line<R> &l) { point<R> pr = projection(l, c.center()); R d = std::norm(c.radius()) - std::norm(pr - c.center()); if (sign(d) == -1) { return {}; } if (sign(d) == 0) { return {pr}; } point<R> e = (l.b - l.a) / std::abs(l.b - l.a); R k = std::sqrt(d); return {pr + e * k, pr - e * k}; } } #line 2 "src/real-geometry/distance/distance-sp.hpp" #line 2 "src/real-geometry/operation/ccw.hpp" #line 2 "src/real-geometry/numbers/ccw.hpp" namespace geometry::number::ccw { constexpr int COUNTER_CLOCKWISE = +1; constexpr int CLOCKWISE = -1; constexpr int ONLINE_BACK = +2; // c-a-b constexpr int ONLINE_FRONT = -2; // a-b-c constexpr int ON_SEGMENT = 0; // a-c-b } #line 2 "src/real-geometry/operation/cross-product.hpp" #line 4 "src/real-geometry/operation/cross-product.hpp" namespace geometry { template< typename R > R cross_product(const vec2d<R> &a, const vec2d<R> &b) { return a.x() * b.y() - a.y() * b.x(); } } #line 8 "src/real-geometry/operation/ccw.hpp" namespace geometry { using namespace geometry::number::ccw; template< typename R > int ccw(const point<R> &a, point<R> b, point<R> c) { b = b - a, c = c - a; if (sign(cross_product(b, c)) == +1) return COUNTER_CLOCKWISE; if (sign(cross_product(b, c)) == -1) return CLOCKWISE; if (sign(inner_product(b, c)) == -1) return ONLINE_BACK; if (std::norm(b) < std::norm(c)) return ONLINE_FRONT; return ON_SEGMENT; } } #line 7 "src/real-geometry/distance/distance-sp.hpp" #line 9 "src/real-geometry/distance/distance-sp.hpp" #include <algorithm> namespace geometry { template< typename R > R distance_sp(const segment<R> &s, const point<R> &p) { point<R> pr = projection({s.a, s.b}, p); if (ccw(s.a, s.b, pr) == 0) return std::abs(pr - p); return std::min(std::abs(s.a - p), std::abs(s.b - p)); } } #line 2 "src/real-geometry/utility/polygon-to-segments.hpp" #line 2 "src/real-geometry/utility/next-idx.hpp" #line 4 "src/real-geometry/utility/next-idx.hpp" namespace geometry { inline usize next_idx(usize idx, usize size) { return idx + 1 == size ? 0 : idx + 1; } } #line 7 "src/real-geometry/utility/polygon-to-segments.hpp" namespace geometry { template< typename R > segments<R> polygon_to_segments(const polygon<R> &poly) { usize n = poly.size(); segments<R> segs(n); for (usize i = 0; i < n; i++) { segs[i] = segment<R>(poly[i], poly[next_idx(i, n)]); } return segs; } } #line 14 "src/real-geometry/area/common-area-circle-polygon.hpp" #line 18 "src/real-geometry/area/common-area-circle-polygon.hpp" namespace geometry::internal { template< typename R > R impl_common_area_ca_cp(const circle<R> &c, const segment<R> &s) { point<R> va = c.o - s.a, vb = c.o - s.b; R f = cross_product(va, vb), res = 0; if (sign(f) == 0) return res; if (sign(std::max(std::abs(va), std::abs(vb)) - c.r) <= 0) return f; point<R> d(inner_product(va, vb), cross_product(va, vb)); if (sign(distance_sp(s, c.o) - c.r) >= 0) { return std::norm(c.r) * std::atan2(d.y(), d.x()); } points<R> ps = cross_point_cl(c, {s.a, s.b}); if (ps.empty()) return res; if (ps.size() == 2 and sign(inner_product<R>(ps[1] - ps[0], s.a - ps[0])) >= 0) { std::swap(ps[0], ps[1]); } ps.emplace(ps.begin(), s.a); ps.emplace_back(s.b); for (usize i = 1; i < ps.size(); i++) { if (equals(ps[i - 1], ps[i])) continue; res += impl_common_area_ca_cp(c, {ps[i - 1], ps[i]}); } return res; } } namespace geometry { template< typename R > R common_area_circle_polygon(const circle<R> &c, const polygon<R> &p) { usize n = p.size(); if (n < 3) return 0; auto segs = polygon_to_segments(p); R res = 0; for (auto &seg: segs) { res += internal::impl_common_area_ca_cp(c, seg); } return res / 2; } }