Adding 3D spheres and some small changes to KMP.

2 files changed, 27 insertions, 1 deletions

diff --git a/math/gcDist.cpp b/math/gcDist.cpp
new file mode 100644
index 0000000..d661744
--- /dev/null
+++ b/math/gcDist.cpp
@@ -0,0 +1,23 @@
+// Great Cirlce Distance mit Längen- und Breitengrad.
+double gcDist(double pLat, double pLon, double qLat, double qLon, double radius) {
+  pLat *= PI / 180; pLon *= PI / 180; qLat *= PI / 180; qLon *= PI / 180;
+  return radius * acos(cos(pLat) * cos(pLon) * cos(qLat) * cos(qLon) +
+                       cos(pLat) * sin(pLon) * cos(qLat) * sin(qLon) +
+                       sin(pLat) * sin(qLat));
+}
+
+// Great Cirlce Distance mit kartesischen Koordinaten.
+double gcDist(point p, point q) {
+  return acos(p.x * q.x + p.y * q.y + p.z * q.z);
+}
+
+// 3D Punkt in kartesischen Koordinaten.
+struct point{
+  double x, y, z;
+  point() {}
+  point(double x, double y, double z) : x(x), y(y), z(z) {}
+  point(double lat, double lon) {
+    lat *= PI / 180.0; lon *= PI / 180.0;
+    x = cos(lat) * sin(lon); y = cos(lat) * cos(lon); z = sin(lat);
+  }
+};
diff --git a/math/math.tex b/math/math.tex
index 51410bd..90e7b3b 100644
--- a/math/math.tex
+++ b/math/math.tex
@@ -176,4 +176,7 @@ Anzahl der Teilmengen von $\mathbb{N}$, die sich zu $n$ aufaddieren mit maximale
 	\#labeled rooted trees			& $n^{n-1}$\\
 	\#labeled unrooted trees		& $n^{n-2}$\\
 	\hline
-\end{tabular}
\ No newline at end of file
+\end{tabular}
+
+\subsection{3D-Kugeln}
+\lstinputlisting{math/gcDist.cpp}