feat: add half-plane intersection

.github/workflows/main.yaml

@@ -2,9 +2,9 @@ name: C++ Formatting
 
 on:
   push:
-    branches: [ master ]
+    branches: [ main ]
   pull_request:
-    branches: [ master ]
+    branches: [ main ]
 
 jobs:
   format:

scripts/format.sh

@@ -1,6 +1,6 @@
 #!/usr/bin/env bash
 root="$(cd "$(dirname "$0")/.." && pwd)"
-target="$root/refcode"
+target="$root/src"
 mapfile -t files < <(find "$target" -type f \( -name '*.cpp' -o -name '*.hpp' \))
 ((${#files[@]})) || { echo "no .cpp/.hpp files in $target"; exit 0; }
 declare -A before

src/5-geometry/half_plane_intersection.cpp

@@ -0,0 +1,60 @@
+#include "../common/common.hpp"
+// INPUT: ln: A vector of directed lines (half-planes).
+// - IMPORTANT: The valid region is to the LEFT of the line (s -> t).
+// - Tip: Add a bounding box (4 lines) if the area might be unbounded.
+// OUTPUT: A vector of vertices representing the intersection polygon.
+// - Order: Counter-Clockwise (CCW).
+// - Returns an empty vector if the intersection is empty or degenerate.
+// TIME COMPLEXITY: O(nlogn)
+struct Point {
+  ld x, y;
+};
+struct Line {
+  Point s, t;
+};
+constexpr ld EPS = 1e-9;
+inline bool equals(ld a, ld b) { return abs(a - b) < EPS; }
+bool line_intersect(Point &s1, Point &e1, Point &s2, Point &e2, Point &v) {
+  ld vx1 = e1.x - s1.x, vy1 = e1.y - s1.y;
+  ld vx2 = e2.x - s2.x, vy2 = e2.y - s2.y;
+  ld det = vx1 * (-vy2) - (-vx2) * vy1;
+  if (equals(det, 0)) return 0;
+  ld s = (ld)((s2.x - s1.x) * (-vy2) + (s2.y - s1.y) * vx2) / det;
+  v.x = s1.x + vx1 * s;
+  v.y = s1.y + vy1 * s;
+  return 1;
+}
+bool bad(Line &a, Line &b, Line &c) {
+  Point v;
+  if (!line_intersect(a.s, a.t, b.s, b.t, v)) return 0;
+  ld crs = (c.t.x - c.s.x) * (v.y - c.s.y) - (c.t.y - c.s.y) * (v.x - c.s.x);
+  return crs < 0 || equals(crs, 0);
+}
+vector<Point> hpi(vector<Line> &ln) {
+  auto lsgn = [&](const Line &a) {
+    if (a.s.y == a.t.y) return a.s.x > a.t.x;
+    return a.s.y > a.t.y;
+  };
+  sort(ln.begin(), ln.end(), [&](const Line &a, const Line &b) {
+    if (lsgn(a) != lsgn(b)) return lsgn(a) < lsgn(b);
+    return (a.t.x - a.s.x) * (b.t.y - b.s.y) - (a.t.y - a.s.y) * (b.t.x - b.s.x) > 0;
+  });
+  deque<Line> dq;
+  for (int i = 0; i < sz(ln); i++) {
+    while (dq.size() >= 2 && bad(dq[dq.size() - 2], dq.back(), ln[i]))
+      dq.pop_back();
+    while (dq.size() >= 2 && bad(dq[0], dq[1], ln[i]))
+      dq.pop_front();
+    if (dq.size() < 2 || !bad(dq.back(), ln[i], dq[0]))
+      dq.push_back(ln[i]);
+  }
+  vector<Point> ret;
+  if (dq.size() >= 3)
+    for (int i = 0; i < sz(dq); i++) {
+      int j = (i + 1) % sz(dq);
+      Point v;
+      if (!line_intersect(dq[i].s, dq[i].t, dq[j].s, dq[j].t, v)) continue;
+      ret.push_back(v);
+    }
+  return ret;
+}

src/common/common.hpp

@@ -4,6 +4,7 @@
 using namespace std;
 
 using ll = long long;
+using ld = long double;
 using pii = pair<int, int>;
 using pll = pair<ll, ll>;