merged

1 files changed, 68 insertions, 0 deletions

diff --git a/geometry/hpi.cpp b/geometry/hpi.cpp
new file mode 100644
index 0000000..3509e0e
--- /dev/null
+++ b/geometry/hpi.cpp
@@ -0,0 +1,68 @@
+constexpr ll inf = 0x1FFF'FFFF'FFFF'FFFF;//THIS CODE IS WIP
+
+bool left(pt p) {return real(p) < 0 || 
+					   (real(p) == 0 && imag(p) < 0);}
+struct hp {
+	pt from, to;
+
+	hp(pt a, pt b) : from(a), to(b) {}
+	hp(pt dummy) : hp(dummy, dummy) {}
+
+	bool dummy() const {return from == to;}
+	pt dir() const {return dummy() ? to : to - from;}
+	bool operator<(const hp& o) const {
+		if (left(dir()) != left(o.dir())) 
+			return left(dir()) > left(o.dir());
+		return cross(dir(), o.dir()) > 0;
+	}
+
+	using lll = __int128;
+	using ptl = complex<lll>;
+	ptl mul(lll m, ptl p) const {return m*p;}//ensure 128bit
+
+	bool check(const hp& a, const hp& b) const {
+		if (dummy() || b.dummy()) return false;
+		if (a.dummy()) {
+			ll ort = sgn(cross(b.dir(), dir()));
+			if (ort == 0) return cross(from, to, a.from) < 0;
+			return cross(b.dir(), a.dir()) * ort > 0;
+		}
+		ll y = cross(a.dir(), b.dir());
+		ll z = cross(b.from - a.from, b.dir());
+		ptl i = mul(y, a.from) + mul(z, a.dir()); //intersect a and b
+		// check if i is outside/right of x
+		return imag(conj(mul(sgn(y),dir()))*(i-mul(y,from))) < 0;
+	}
+};
+
+constexpr ll lim = 2e9+7;
+
+deque<hp> intersect(vector<hp> hps) {
+	hps.push_back(hp(pt{lim+1,-1}));
+	hps.push_back(hp(pt{lim+1,1}));
+	sort(all(hps));
+
+	deque<hp> dq = {hp(pt{-lim, 1})};
+	for (auto x : hps) {
+		while (sz(dq) > 1 && x.check(dq.end()[-1], dq.end()[-2]))
+			dq.pop_back();
+		while (sz(dq) > 1 && x.check(dq[0], dq[1]))
+			dq.pop_front();
+
+		if (cross(x.dir(), dq.back().dir()) == 0) {
+			if (dot(x.dir(), dq.back().dir()) < 0) return {};
+			if (cross(x.from, x.to, dq.back().from) < 0)
+				dq.pop_back();
+			else continue;
+		}
+		dq.push_back(x);
+	}
+
+	while (sz(dq) > 2 && dq[0].check(dq.end()[-1], dq.end()[-2]))
+		dq.pop_back();
+	while (sz(dq) > 2 && dq.end()[-1].check(dq[0], dq[1]))
+		dq.pop_front();
+
+	if (sz(dq) < 3) return {};
+	return dq;
+}