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source/Geometry/HPI.cpp

@@ -0,0 +1,50 @@
+using ld = long double;
+using pdd = pair<ld, ld>;
+using line = pair<pdd, pdd>; // half plane : left side of vector fi->se
+
+const ld eps = 1e-9;
+pdd operator*(const pdd& a, ld s) { return {a.fi * s, a.se * s}; }
+inline bool equals(ld a, ld b) { return abs(a - b) < eps; }
+
+bool line_intersect(line& a, line& b, pdd& v) {
+    ld det = (a.se - a.fi) / (b.se - b.fi);
+    if (equals(det, 0)) return 0;
+    ld t = ((b.fi - a.fi) / (b.se - b.fi)) / det; 
+    v = a.fi + (a.se - a.fi) * t;
+    return 1;
+}
+
+bool bad(line& a, line& b, line& c) {
+    pdd v; if(!line_intersect(a, b, v)) return 0;
+    return (c.se - c.fi) / (v - c.fi) <= eps;
+}
+
+vector<pdd> HPI(vector<line>& lns) {
+    auto lsgn = [&](const line& a) {
+        if(a.fi.se == a.se.se) return a.fi.fi > a.se.fi;
+        return a.fi.se > a.se.se;
+    };
+    sort(lns.begin(), lns.end(), [&](const line& a, const line& b) {
+        if(lsgn(a) != lsgn(b)) return lsgn(a) < lsgn(b);
+        return (a.se - a.fi) / (b.se - b.fi) > 0;
+    });
+    
+    deque<line> dq;
+    for(auto l : lns){
+        while(dq.size() >= 2 && bad(dq[dq.size()-2], dq.back(), l)) dq.pop_back();
+        while(dq.size() >= 2 && bad(dq[0], dq[1], l)) dq.pop_front();
+        
+        if(dq.size() < 2 || !bad(dq.back(), l, dq[0])) dq.pb(l);
+    }
+    
+    vector<pdd> res;
+    if(dq.size() >= 3) {
+        for(int i = 0; i < (int)dq.size(); i++) {
+            int j = (i + 1) % (int)dq.size();
+            pdd v;
+            if(!line_intersect(dq[i], dq[j], v)) continue;
+            res.push_back(v);
+        }
+    }
+    return res;
+}