線分アレンジメント (src/Geometry/SegmentArrangement.hpp)

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Last update: 2024-09-28 19:54:09+09:00
Include: #include "src/Geometry/SegmentArrangement.hpp"

`SegmentArrangement<K>` クラス

二次元空間上の線分の端点および交点を頂点とし, 線分上をたどって辿り着ける点どうしが連結するように辺を張ってグラフを構築する線分アレンジメントを doubly connected edge list (DCEL) で表現するクラス.

メンバ関数	概要
`SegmentArrangement(ss)`	コンストラクタ. `vector<Segment<K>>` を引数にとる. 線分アレンジメントを実行.
`vertex_size()`	頂点数を返す.
`face_size()`	面数を返す.
`out_edges(v)`	頂点 v から出る辺を隣接リストのように返す.
`point(v)`	頂点 v に対応する二次元空間上の点 ( `Point<K>` クラス ) を返す.
`vertex(p)`	二次元空間上の点 ( `Point<K>` クラス ) $\boldsymbol{p}$ に対応する頂点番号を返す.
`to_v(e)`	有向辺 e の行き先の頂点を返す.
`from_v(e)`	有向辺 e が出てくる頂点を返す.
`twin(e)`	有向辺 e の頂点を逆にした有向辺を返す.
`next(e)`	有向辺 e の次の有向辺を返す. この順というのは反時計回りに多角形面の辺を辿る順を指す.
`prev(e)`	有向辺 e の前の有向辺を返す. この順というのは反時計回りに多角形面の辺を辿る順を指す.
`incident_face(e)`	有向辺 e が面している面番号を返す.
`component_e(f)`	面 f を構成する辺の一つを返す.
`area2(f)`	面 f の面積の二倍を返す. 面 f が有界でないなら値は負になる.
`area(f)`	面 f の面積を返す. 面 f が有界でないなら値は負になる.
`is_outside(f)`	面 f が有界でないならtrueを返す.

参考

https://en.wikipedia.org/wiki/Doubly_connected_edge_list

Depends on

Verified with

Code

#pragma once
#include <algorithm>
#include <unordered_set>
#include "src/Geometry/Segment.hpp"
#include "src/Geometry/angle.hpp"
#include "src/Internal/ListRange.hpp"
namespace geo {
template <class K> class SegmentArrangement {
 vector<Point<K>> ps;
 vector<int> dst, pr, nx, icf, cmp, g, pos;
public:
 SegmentArrangement(const vector<Segment<K>> &ss) {
  for (const auto &s: ss) ps.push_back(s.p), ps.push_back(s.q);
  for (int i= ss.size(); i--;)
   for (int j= i; j--;)
    if (auto cp= cross_points(ss[i], ss[j]); cp.size()) ps.insert(ps.end(), cp.begin(), cp.end());
  sort(ps.begin(), ps.end()), ps.erase(unique(ps.begin(), ps.end()), ps.end());
  const int n= ps.size();
  unordered_set<int> st;
  for (const auto &s: ss) {
   vector<int> l;
   for (int i= n; i--;)
    if (s.on(ps[i])) l.push_back(i);
   sort(l.begin(), l.end(), [&](int i, int j) { return ps[i] < ps[j]; });
   for (int i= l.size(); --i;) {
    auto [u, v]= minmax(l[i], l[i - 1]);
    if (int a= (u << 16) | v; !st.count(a)) st.insert(a), dst.push_back(u), dst.push_back(v);
   }
  }
  const int m= dst.size();
  pos.resize(n + 1), g.resize(m), icf.assign(m, -1), pr.resize(m), nx.resize(m);
  for (int v: dst) ++pos[v];
  for (int v= 0; v < n; ++v) pos[v + 1]+= pos[v];
  for (int e= m; e--;) g[--pos[dst[e ^ 1]]]= e;
  vector<Point<K>> qs(m);
  for (int e= m; e--;) qs[e]= ps[dst[e]] - ps[dst[e ^ 1]];
  AngleComp<K> ac;
  auto cm= [&](int i, int j) { return ac(qs[i], qs[j]); };
  vector<int> nxi(m), pri(m);
  for (int v= n; v--;) {
   sort(g.begin() + pos[v], g.begin() + pos[v + 1], cm);
   for (int i= pos[v] + 1; i < pos[v + 1]; ++i) nxi[g[i - 1]]= g[i], pri[g[i]]= g[i - 1];
   nxi[g[pos[v + 1] - 1]]= g[pos[v]], pri[g[pos[v]]]= g[pos[v + 1] - 1];
  }
  for (int e= m; e--;) nx[e]= pri[e ^ 1], pr[e]= nxi[e] ^ 1;
  for (int e= m; e--;) {
   if (icf[e] != -1) continue;
   int f= cmp.size(), x= e;
   cmp.push_back(e);
   do {
    icf[x]= f, x= nx[x];
   } while (x != e);
  }
 }
 size_t vertex_size() const { return ps.size(); }
 size_t face_size() const { return cmp.size(); }
 ConstListRange<int> out_edges(int v) const { return {g.cbegin() + pos[v], g.cbegin() + pos[v + 1]}; }
 Point<K> point(int v) const { return ps[v]; }
 int vertex(const Point<K> &p) const { return lower_bound(ps.begin(), ps.end(), p) - ps.begin(); }
 int to_v(int e) const { return dst[e]; }
 int from_v(int e) const { return dst[e ^ 1]; }
 int twin(int e) const { return e ^ 1; }
 int next(int e) const { return nx[e]; }
 int prev(int e) const { return pr[e]; }
 int incident_face(int e) const { return icf[e]; }
 int component_e(int f) const { return cmp[f]; }
 K area2(int f) const {
  K a= 0;
  for (int e= cmp[f], ne= nx[e];; ne= nx[e= ne]) {
   a+= cross(ps[dst[e]], ps[dst[ne]]);
   if (ne == cmp[f]) break;
  }
  return a;
 }
 K area(int f) const { return area2(f) / 2; }
 bool is_outside(int f) const { return area2(f) < 0; }
};
}

#line 2 "src/Geometry/SegmentArrangement.hpp"
#include <algorithm>
#include <unordered_set>
#line 2 "src/Geometry/Line.hpp"
#include <vector>
#line 2 "src/Geometry/Point.hpp"
#include <iostream>
#include <fstream>
#include <iomanip>
#include <cmath>
#include <cassert>
#line 2 "src/Internal/long_traits.hpp"
// clang-format off
template<class T>struct make_long{using type= T;};
template<>struct make_long<char>{using type= short;};
template<>struct make_long<unsigned char>{using type= unsigned short;};
template<>struct make_long<short>{using type= int;};
template<>struct make_long<unsigned short>{using type= unsigned;};
template<>struct make_long<int>{using type= long long;};
template<>struct make_long<unsigned>{using type= unsigned long long;};
template<>struct make_long<long long>{using type= __int128_t;};
template<>struct make_long<unsigned long long>{using type= __uint128_t;};
template<>struct make_long<float>{using type= double;};
template<>struct make_long<double>{using type= long double;};
template<class T> using make_long_t= typename make_long<T>::type;
// clang-format on
#line 8 "src/Geometry/Point.hpp"
namespace geo {
using namespace std;
struct Visualizer {
 ofstream ofs;
 Visualizer(string s= "visualize.txt"): ofs(s) { ofs << fixed << setprecision(10); }
 friend Visualizer &operator<<(Visualizer &vis, const string &s) { return vis.ofs << s, vis; }
};
template <class K> int sgn(K x) {
 if constexpr (is_floating_point_v<K>) {
  static constexpr K EPS= 1e-9;
  return x < -EPS ? -1 : x > EPS;
 } else return x < 0 ? -1 : x > 0;
}
template <class K> K err_floor(K x) {
 K y= floor(x);
 if constexpr (is_floating_point_v<K>)
  if (K z= y + 1, w= x - z; 0 <= sgn(w) && sgn(w - 1) < 0) return z;
 return y;
}
template <class K> K err_ceil(K x) {
 K y= ceil(x);
 if constexpr (is_floating_point_v<K>)
  if (K z= y - 1, w= x - z; 0 < sgn(w + 1) && sgn(w) <= 0) return z;
 return y;
}
template <class K> struct Point {
 K x, y;
 Point(K x= K(), K y= K()): x(x), y(y) {}
 Point &operator+=(const Point &p) { return x+= p.x, y+= p.y, *this; }
 Point &operator-=(const Point &p) { return x-= p.x, y-= p.y, *this; }
 Point &operator*=(K a) { return x*= a, y*= a, *this; }
 Point &operator/=(K a) { return x/= a, y/= a, *this; }
 Point operator+(const Point &p) const { return {x + p.x, y + p.y}; }
 Point operator-(const Point &p) const { return {x - p.x, y - p.y}; }
 Point operator*(K a) const { return {x * a, y * a}; }
 Point operator/(K a) const { return {x / a, y / a}; }
 friend Point operator*(K a, const Point &p) { return {a * p.x, a * p.y}; }
 Point operator-() const { return {-x, -y}; }
 bool operator<(const Point &p) const {
  int s= sgn(x - p.x);
  return s ? s < 0 : sgn(y - p.y) < 0;
 }
 bool operator>(const Point &p) const { return p < *this; }
 bool operator<=(const Point &p) const { return !(p < *this); }
 bool operator>=(const Point &p) const { return !(*this < p); }
 bool operator==(const Point &p) const { return !sgn(x - p.x) && !sgn(y - p.y); }
 bool operator!=(const Point &p) const { return sgn(x - p.x) || sgn(y - p.y); }
 Point operator!() const { return {-y, x}; }  // rotate 90 degree
 friend istream &operator>>(istream &is, Point &p) { return is >> p.x >> p.y; }
 friend ostream &operator<<(ostream &os, const Point &p) { return os << "(" << p.x << ", " << p.y << ")"; }
 friend Visualizer &operator<<(Visualizer &vis, const Point &p) { return vis.ofs << p.x << " " << p.y << "\n", vis; }
};
template <class K> make_long_t<K> dot(const Point<K> &p, const Point<K> &q) { return make_long_t<K>(p.x) * q.x + make_long_t<K>(p.y) * q.y; }
// left turn: > 0, right turn: < 0
template <class K> make_long_t<K> cross(const Point<K> &p, const Point<K> &q) { return make_long_t<K>(p.x) * q.y - make_long_t<K>(p.y) * q.x; }
template <class K> make_long_t<K> norm2(const Point<K> &p) { return dot(p, p); }
template <class K> long double norm(const Point<K> &p) { return sqrt(norm2(p)); }
template <class K> make_long_t<K> dist2(const Point<K> &p, const Point<K> &q) { return norm2(p - q); }
template <class T, class U> long double dist(const T &a, const U &b) { return sqrt(dist2(a, b)); }
enum CCW { COUNTER_CLOCKWISE, CLOCKWISE, ONLINE_BACK, ONLINE_FRONT, ON_SEGMENT };
ostream &operator<<(ostream &os, CCW c) { return os << (c == COUNTER_CLOCKWISE ? "COUNTER_CLOCKWISE" : c == CLOCKWISE ? "CLOCKWISE" : c == ONLINE_BACK ? "ONLINE_BACK" : c == ONLINE_FRONT ? "ONLINE_FRONT" : "ON_SEGMENT"); }
template <class K> CCW ccw(const Point<K> &p0, const Point<K> &p1, const Point<K> &p2) {
 Point a= p1 - p0, b= p2 - p0;
 int s;
 if constexpr (is_floating_point_v<K>) s= sgn(sgn(cross(a, b) / sqrt(norm2(a) * norm2(b))));
 else s= sgn(cross(a, b));
 if (s) return s > 0 ? COUNTER_CLOCKWISE : CLOCKWISE;
 if (K d= dot(a, b); sgn(d) < 0) return ONLINE_BACK;
 else return sgn(d - norm2(a)) > 0 ? ONLINE_FRONT : ON_SEGMENT;
}
template <class K> struct Line;
template <class K> struct Segment;
template <class K> class Polygon;
template <class K> struct Convex;
template <class K> struct Affine {
 K a00= 1, a01= 0, a10= 0, a11= 1;
 Point<K> b;
 Point<K> operator()(const Point<K> &p) const { return {a00 * p.x + a01 * p.y + b.x, a10 * p.x + a11 * p.y + b.y}; }
 Line<K> operator()(const Line<K> &l);
 Segment<K> operator()(const Segment<K> &s);
 Polygon<K> operator()(const Polygon<K> &p);
 Convex<K> operator()(const Convex<K> &c);
 Affine operator*(const Affine &r) const { return {a00 * r.a00 + a01 * r.a10, a00 * r.a01 + a01 * r.a11, a10 * r.a00 + a11 * r.a10, a10 * r.a01 + a11 * r.a11, (*this)(r)}; }
 Affine &operator*=(const Affine &r) { return *this= *this * r; }
};
template <class K> Affine<K> translate(const Point<K> &p) { return {1, 0, 0, 1, p}; }
}
#line 4 "src/Geometry/Line.hpp"
namespace geo {
template <class K> struct Line {
 using P= Point<K>;
 P p, d;  // p+td
 Line() {}
 // p + td
 Line(const P &p, const P &d): p(p), d(d) { assert(sgn(norm2(d))); }
 // ax+by+c=0 ................. ax+by+c>0: left, ax+by+c=0: on, ax+by+c<0: right
 Line(K a, K b, K c) {
  int sa= sgn(a), sb= sgn(b);
  assert(sa || sb);
  d= P{b, -a}, p= sb ? P{0, -c / b} : P{-c / a, 0};
 }
 bool operator==(const Line &l) const { return !sgn(cross(d, l.d)) && !where(l.p); }
 bool operator!=(const Line &l) const { return sgn(cross(d, l.d)) || where(l.p); }
 // +1: left, 0: on, -1: right
 int where(const P &q) const { return sgn(cross(d, q - p)); }
 P project(const P &q) const { return p + dot(q - p, d) / norm2(d) * d; }
 // return  a,b,c of ax+by+c=0
 tuple<K, K, K> coef() const { return make_tuple(-d.y, d.x, cross(p, d)); }
 friend ostream &operator<<(ostream &os, const Line &l) { return os << l.p << " + t" << l.d; }
 friend Visualizer &operator<<(Visualizer &vis, const Line &l) {
  auto [a, b, c]= l.coef();
  return vis.ofs << "Line " << a << " " << b << " " << c << "\n", vis;
 }
};
// p + t(q-p)
template <class K> Line<K> line_through(const Point<K> &p, const Point<K> &q) { return Line(p, q - p); }
template <class K> bool is_parallel(const Line<K> &l, const Line<K> &m) { return !sgn(cross(l.d, m.d)); }
template <class K> bool is_orthogonal(const Line<K> &l, const Line<K> &m) { return !sgn(dot(l.d, m.d)); }
// 1 : properly crossing, 0 : disjoint parallel, 2 : same line
template <class K> vector<Point<K>> cross_points(const Line<K> &l, const Line<K> &m) {
 K a= cross(m.d, l.d), b= cross(l.p - m.p, l.d);
 if (sgn(a)) return {m.p + b / a * m.d};  // properly crossing
 if (sgn(b)) return {};                   // disjoint parallel
 return {m.p, m.p + m.d};                 // same line
}
// perpendicular bisector ............ p on leftside
template <class K> Line<K> bisector(const Point<K> &p, const Point<K> &q) { return Line((p + q) / 2, !(q - p)); }
// angle bisector ........... parallel -> 1 line, non-parallel -> 2 lines
template <class K> vector<Line<K>> bisector(const Line<K> &l, const Line<K> &m) {
 auto cp= cross_points(l, m);
 if (cp.size() != 1) return {Line((l.p + m.p) / 2, l.d)};
 auto d= l.d / norm(l.d) + m.d / norm(m.d);
 return {Line(cp[0], d), Line(cp[0], !d)};
}
template <class K> make_long_t<K> dist2(const Line<K> &l, const Point<K> &p) {
 make_long_t<K> a= cross(l.d, p - l.p);
 return a * a / norm2(l.d);
}
template <class K> make_long_t<K> dist2(const Point<K> &p, const Line<K> &l) { return dist2(l, p); }
template <class K> make_long_t<K> dist2(const Line<K> &l, const Line<K> &m) { return is_parallel(l, m) ? dist2(l, m.p) : 0; }
template <class K> Affine<K> reflect(const Line<K> &l) {
 K a= l.d.x * l.d.x, b= l.d.x * l.d.y * 2, c= l.d.y * l.d.y, d= a + c;
 a/= d, b/= d, c/= d, d= a - c;
 return {d, b, b, -d, Point<K>{c * 2 * l.p.x - b * l.p.y, a * 2 * l.p.y - b * l.p.x}};
}
template <class K> Line<K> Affine<K>::operator()(const Line<K> &l) { return line_through((*this)(l.p), (*this)(l.p + l.d)); }
}
#line 4 "src/Geometry/Segment.hpp"
namespace geo {
template <class K> struct Segment {
 using P= Point<K>;
 P p, q;
 Segment() {}
 Segment(const P &p, const P &q): p(p), q(q) {}
 // do not consider the direction
 bool operator==(const Segment &s) const { return (p == s.p && q == s.q) || (p == s.q && q == s.p); }
 bool operator!=(const Segment &s) const { return !(*this == s); }
 bool on(const P &r) const { return ccw(p, q, r) == ON_SEGMENT; }
 P &operator[](int i) { return i ? q : p; }
 const P &operator[](int i) const { return i ? q : p; }
 long double length() const { return dist(p, q); }
 P closest_point(const P &r) const {
  P d= q - p;
  K a= dot(r - p, d), b;
  return sgn(a) > 0 ? sgn(a - (b= norm2(d))) < 0 ? p + a / b * d : q : p;
 }
 friend ostream &operator<<(ostream &os, const Segment &s) { return os << s.p << "---" << s.q; }
 friend Visualizer &operator<<(Visualizer &vis, const Segment &s) { return vis.ofs << "Segment " << s.p.x << " " << s.p.y << " " << s.q.x << " " << s.q.y << "\n", vis; }
};
// 1: properly crossing, 0: no intersect, 2: same line
template <class K> vector<Point<K>> cross_points(const Segment<K> &s, const Line<K> &l) {
 Point d= s.q - s.p;
 K a= cross(d, l.d), b= cross(l.p - s.p, l.d);
 if (sgn(a)) {
  if (b/= a; sgn(b) < 0 || sgn(b - 1) > 0) return {};  // no intersect
  else return {s.p + b * d};                           // properly crossing}
 }
 if (sgn(b)) return {};  // disjoint parallel
 return {s.p, s.q};      // same line
}
template <class K> vector<Point<K>> cross_points(const Line<K> &l, const Segment<K> &s) { return cross_points(s, l); }
// 2: same line, 0: no intersect, 1: ...
template <class K> vector<Point<K>> cross_points(const Segment<K> &s, const Segment<K> &t) {
 Point d= s.q - s.p, e= t.q - t.p;
 K a= cross(d, e), b= cross(t.p - s.p, e);
 if (sgn(a)) {
  if (b/= a; sgn(b) < 0 || sgn(b - 1) > 0) return {};                       // no intersect
  if (b= cross(d, s.p - t.p) / a; sgn(b) < 0 || sgn(b - 1) > 0) return {};  // no intersect
  return {t.p + b * e};                                                     // properly crossing
 }
 if (sgn(b)) return {};  // disjoint parallel
 vector<Point<K>> ps;    // same line
 auto insert_if_possible= [&](const Point<K> &p) {
  for (auto q: ps)
   if (p == q) return;
  ps.emplace_back(p);
 };
 if (sgn(dot(t.p - s.p, t.q - s.p)) <= 0) insert_if_possible(s.p);
 if (sgn(dot(t.p - s.q, t.q - s.q)) <= 0) insert_if_possible(s.q);
 if (sgn(dot(s.p - t.p, s.q - t.p)) <= 0) insert_if_possible(t.p);
 if (sgn(dot(s.p - t.q, s.q - t.q)) <= 0) insert_if_possible(t.q);
 return ps;
}
enum INTERSECTION { CROSSING, TOUCHING, DISJOINT, OVERLAP };
ostream &operator<<(ostream &os, INTERSECTION i) { return os << (i == CROSSING ? "CROSSING" : i == TOUCHING ? "TOUCHING" : i == DISJOINT ? "DISJOINT" : "OVERLAP"); }
template <class K> INTERSECTION intersection(const Segment<K> &s, const Segment<K> &t) {
 auto cp= cross_points(s, t);
 return cp.size() == 0 ? DISJOINT : cp.size() == 2 ? OVERLAP : cp[0] == s.p || cp[0] == s.q || cp[0] == t.p || cp[0] == t.q ? TOUCHING : CROSSING;
}
template <class K> make_long_t<K> dist2(const Segment<K> &s, const Point<K> &p) { return dist2(p, s.closest_point(p)); }
template <class K> make_long_t<K> dist2(const Point<K> &p, const Segment<K> &s) { return dist2(s, p); }
template <class K> make_long_t<K> dist2(const Segment<K> &s, const Line<K> &l) { return cross_points(s, l).size() ? 0 : min(dist2(s.p, l), dist2(s.q, l)); }
template <class K> make_long_t<K> dist2(const Line<K> &l, const Segment<K> &s) { return dist2(s, l); }
template <class K> make_long_t<K> dist2(const Segment<K> &s, const Segment<K> &t) { return cross_points(s, t).size() ? 0 : min({dist2(s, t.p), dist2(s, t.q), dist2(t, s.p), dist2(t, s.q)}); }
template <class K> Segment<K> Affine<K>::operator()(const Segment<K> &s) { return {(*this)(s.p), (*this)(s.q)}; }
}
#line 4 "src/Geometry/angle.hpp"
namespace geo {
long double radian_to_degree(long double r) { return r * 180.0 / M_PI; }
long double degree_to_radian(long double d) { return d * M_PI / 180.0; }
long double normalize_radian(long double r) { return r= fmod(r + M_PI, 2 * M_PI), r > 0 ? r - M_PI : r + M_PI; }
template <class K> long double angle(const Point<K> &p) { return atan2(p.y, p.x); }
template <class K> long double angle(const Point<K> &p, const Point<K> &q) { return atan2(cross(p, q), dot(p, q)); }
template <class K> Affine<K> rotate(long double theta) {
 K c= cos(theta), s= sin(theta);
 return {c, -s, s, c, Point<K>{0, 0}};
}
template <class K> Affine<K> rotate(const Point<K> &p, long double theta) {
 K c= cos(theta), s= sin(theta);
 return {c, -s, s, c, Point<K>{p.x - c * p.x + s * p.y, p.y - s * p.x - c * p.y}};
}
template <class K> Affine<K> rotate90(const Point<K> &p) { return {0, -1, 1, 0, p - !p}; }
// (-PI,PI], counter-clockwise
template <class K> class AngleComp {
 using P= Point<K>;
 static int quad(const P &p) {
  if (int s= sgn(p.y); s) return s;
  return sgn(p.x) < 0 ? 2 : 0;
 }
public:
 bool operator()(const P &p, const P &q) const {
  if (int a= quad(p), b= quad(q); a != b) return a < b;
  return cross(p, q) > 0;
 }
};
}
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 7 "src/Geometry/SegmentArrangement.hpp"
namespace geo {
template <class K> class SegmentArrangement {
 vector<Point<K>> ps;
 vector<int> dst, pr, nx, icf, cmp, g, pos;
public:
 SegmentArrangement(const vector<Segment<K>> &ss) {
  for (const auto &s: ss) ps.push_back(s.p), ps.push_back(s.q);
  for (int i= ss.size(); i--;)
   for (int j= i; j--;)
    if (auto cp= cross_points(ss[i], ss[j]); cp.size()) ps.insert(ps.end(), cp.begin(), cp.end());
  sort(ps.begin(), ps.end()), ps.erase(unique(ps.begin(), ps.end()), ps.end());
  const int n= ps.size();
  unordered_set<int> st;
  for (const auto &s: ss) {
   vector<int> l;
   for (int i= n; i--;)
    if (s.on(ps[i])) l.push_back(i);
   sort(l.begin(), l.end(), [&](int i, int j) { return ps[i] < ps[j]; });
   for (int i= l.size(); --i;) {
    auto [u, v]= minmax(l[i], l[i - 1]);
    if (int a= (u << 16) | v; !st.count(a)) st.insert(a), dst.push_back(u), dst.push_back(v);
   }
  }
  const int m= dst.size();
  pos.resize(n + 1), g.resize(m), icf.assign(m, -1), pr.resize(m), nx.resize(m);
  for (int v: dst) ++pos[v];
  for (int v= 0; v < n; ++v) pos[v + 1]+= pos[v];
  for (int e= m; e--;) g[--pos[dst[e ^ 1]]]= e;
  vector<Point<K>> qs(m);
  for (int e= m; e--;) qs[e]= ps[dst[e]] - ps[dst[e ^ 1]];
  AngleComp<K> ac;
  auto cm= [&](int i, int j) { return ac(qs[i], qs[j]); };
  vector<int> nxi(m), pri(m);
  for (int v= n; v--;) {
   sort(g.begin() + pos[v], g.begin() + pos[v + 1], cm);
   for (int i= pos[v] + 1; i < pos[v + 1]; ++i) nxi[g[i - 1]]= g[i], pri[g[i]]= g[i - 1];
   nxi[g[pos[v + 1] - 1]]= g[pos[v]], pri[g[pos[v]]]= g[pos[v + 1] - 1];
  }
  for (int e= m; e--;) nx[e]= pri[e ^ 1], pr[e]= nxi[e] ^ 1;
  for (int e= m; e--;) {
   if (icf[e] != -1) continue;
   int f= cmp.size(), x= e;
   cmp.push_back(e);
   do {
    icf[x]= f, x= nx[x];
   } while (x != e);
  }
 }
 size_t vertex_size() const { return ps.size(); }
 size_t face_size() const { return cmp.size(); }
 ConstListRange<int> out_edges(int v) const { return {g.cbegin() + pos[v], g.cbegin() + pos[v + 1]}; }
 Point<K> point(int v) const { return ps[v]; }
 int vertex(const Point<K> &p) const { return lower_bound(ps.begin(), ps.end(), p) - ps.begin(); }
 int to_v(int e) const { return dst[e]; }
 int from_v(int e) const { return dst[e ^ 1]; }
 int twin(int e) const { return e ^ 1; }
 int next(int e) const { return nx[e]; }
 int prev(int e) const { return pr[e]; }
 int incident_face(int e) const { return icf[e]; }
 int component_e(int f) const { return cmp[f]; }
 K area2(int f) const {
  K a= 0;
  for (int e= cmp[f], ne= nx[e];; ne= nx[e= ne]) {
   a+= cross(ps[dst[e]], ps[dst[ne]]);
   if (ne == cmp[f]) break;
  }
  return a;
 }
 K area(int f) const { return area2(f) / 2; }
 bool is_outside(int f) const { return area2(f) < 0; }
};
}

線分アレンジメント (src/Geometry/SegmentArrangement.hpp)

SegmentArrangement<K> クラス

参考

Depends on

Verified with

Code

`SegmentArrangement<K>` クラス