1 files changed, 33 insertions, 0 deletions
diff --git a/geometry/polygon.cpp b/geometry/polygon.cpp
new file mode 100644
index 0000000..6a8080d
--- /dev/null
+++ b/geometry/polygon.cpp
@@ -0,0 +1,33 @@
+// Berechnet den Flächeninhalt eines Polygons
+// (nicht selbstschneidend).
+// Punkte gegen den Uhrzeigersinn: positiv, sonst negativ.
+double area(const vector<pt>& polygon) {//points unique
+	double res = 0; int n = sz(polygon);
+	for (int i = 0; i < n; i++)
+		res += cross(polygon[i], polygon[(i + 1) % n]);
+	return 0.5 * res;
+}
+
+// Testet, ob ein Punkt im Polygon liegt (beliebige Polygone).
+bool inside(pt p, const vector<pt>& polygon) {//points unique
+	pt rayEnd = p + pt(1, 1000000);
+	int counter = 0, n = sz(polygon);
+	for (int i = 0; i < n; i++) {
+		pt start = polygon[i], end = polygon[(i + 1) % n];
+		if (lineSegmentIntersection(p, rayEnd, start, end)) {
+			counter++;
+	}}
+	return counter & 1;
+}
+
+//convex hull without duplicates, h[0] == h.back()
+bool inside(pt p, const vector<pt>& hull) {
+	if (orientation(hull[0], hull.back(), p) > 0) return false;
+	ll l = 0, r = sz(hull) - 1;
+	while (l + 1 < r) {
+		ll m = (l + r) / 2;
+		if (orientation(hull[0], hull[m], p) >= 0) l = m;
+		else r = m;
+	}
+	return orientation(hull[l], hull[r], p) >= 0;
+}