From 1d2d2541dd913892a983da13f84c33f1a5d43ff6 Mon Sep 17 00:00:00 2001
From: Paul Jungeblut <s_jungeb@i08pc58.atis-stud.uni-karlsruhe.de>
Date: Tue, 11 Nov 2014 15:25:06 +0100
Subject: geometrische Formeln

---
 geometry/formulars.cpp |  58 +++++++++++++++++++++++++++++++++++++++++++++++++
 geometry/geometry.tex  |   7 ++++--
 graph/graph.tex        |   2 +-
 math/binomial.cpp      |  14 +++---------
 math/math.tex          |   4 ++++
 tcr.pdf                | Bin 117854 -> 220754 bytes
 tcr.tex                |   1 +
 7 files changed, 72 insertions(+), 14 deletions(-)
 create mode 100644 geometry/formulars.cpp
 create mode 100644 math/math.tex

diff --git a/geometry/formulars.cpp b/geometry/formulars.cpp
new file mode 100644
index 0000000..6984be9
--- /dev/null
+++ b/geometry/formulars.cpp
@@ -0,0 +1,58 @@
+//komplexe Zahlen als Darstellung fuer Punkte
+typedef pt complex<double>;
+//Winkel zwischen Punkt und x-Achse in [0, 2 * PI), Winkel zwischen a und b
+double angle = arg (a), angle_a_b = arg (a - b);
+//Punkt rotiert um Winkel theta
+pt a_rotated = a * exp (pt (0, theta));
+//Mittelpunkt des Dreiecks abc
+pt centroid = (a + b + c) / 3;
+//Skalarprodukt
+double dot(pt a, pt b) {
+	return real(conj(a) * b);
+}
+//Kreuzprodukt, 0, falls kollinear
+double cross(pt a, pt b) {
+	return imag(conj(a) * b);
+}
+//wenn Eckpunkte bekannt
+double areaOfTriangle(pt a, pt b, pt c) {
+	return abs(cross(b - a, c - a)) / 2.0;
+}
+//wenn Seitenlaengen bekannt
+double areaOfTriangle(double a, double b, double c) {
+	double s = (a + b + c) / 2;
+	return sqrt(s * (s-a) * (s-b) * (s-c));
+}
+// Sind die Dreiecke a1, b1, c1, and a2, b2, c2 aehnlich?
+// Erste Zeile testet Aehnlichkeit mit gleicher Orientierung,
+// zweite Zeile testst Aehnlichkeit mit unterschiedlicher Orientierung
+bool similar (pt a1, pt b1, pt c1, pt a2, pt b2, pt c2) {
+	return (
+		(b2 - a2) * (c1 - a1) == (b1 - a1) * (c2 - a2) ||
+		(b2 - a2) * (conj (c1) - conj (a1)) == (conj (b1) - conj (a1)) * (c2 - a2)
+	);
+}
+//Linksknick von a->b nach a->c
+double ccw(pt a, pt b, pt c) {
+	return cross(b - a, c - a); //<0 => falls Rechtsknick, 0 => kollinear, >0 => Linksknick
+}
+//Streckenschnitt, Strecken a-b und c-d
+bool lineSegmentIntersection(pt a, pt b, pt c, pt d) {
+	if (ccw(a, b, c) == 0 && ccw(a, b, d) == 0) { //kollinear
+		double dist = abs(a - b);
+		return (abs(a - c) <= dist && abs(b - c) <= dist) || (abs(a - d) <= dist && abs(b - d) <= dist);
+	}
+	return ccw(a, b, c) * ccw(a, b, d) <= 0 && ccw(c, d, a) * ccw(c, d, b) <= 0;
+}
+//Entfernung von p zu a-b
+double distToLine(pt a, pt b, pt p) {
+	return abs(cross(p - a, b - a)) / abs(b - a);
+}
+//liegt p auf a-b
+bool pointOnLine(pt a, pt b, pt p) {
+	return abs(distToLine(a, b, p)) < EPSILON;
+}
+//testet, ob d in der gleichen Ebene liegt wie a, b, und c
+bool isCoplanar(pt a, pt b, pt c, pt d) {
+	return (b - a) * (c - a) * (d - a) == 0;
+}
\ No newline at end of file
diff --git a/geometry/geometry.tex b/geometry/geometry.tex
index 7a72526..6192c6e 100644
--- a/geometry/geometry.tex
+++ b/geometry/geometry.tex
@@ -1,4 +1,7 @@
-\section{Geometry}
+\section{Geometrie}
 
 \subsection{Closest Pair}
-\lstinputlisting{geometry/closestPair.cpp}
\ No newline at end of file
+\lstinputlisting{geometry/closestPair.cpp}
+
+\subsection{Formeln - \lstinline{std::complex}}
+\lstinputlisting{geometry/formulars.cpp}
\ No newline at end of file
diff --git a/graph/graph.tex b/graph/graph.tex
index 1c37bc7..53cfb2a 100644
--- a/graph/graph.tex
+++ b/graph/graph.tex
@@ -1,4 +1,4 @@
-\section{Graph}
+\section{Graphen}
 
 \subsection{Strongly Connected Components (\textsc{Tarjans}-Algorithmus)}
 \lstinputlisting{graph/scc.cpp}
diff --git a/math/binomial.cpp b/math/binomial.cpp
index afc9800..61d9d69 100644
--- a/math/binomial.cpp
+++ b/math/binomial.cpp
@@ -1,15 +1,7 @@
-#include <iostream>
-
-using namespace std;
-
-
-unsigned long long calc_binom(unsigned long long N, unsigned long long K)
-{
-   unsigned long long r = 1;
-   unsigned long long d;
+ll calc_binom(ll N, ll K) {
+   ll r = 1, d;
    if (K > N) return 0;
-   for (d = 1; d <= K; d++)
-   {
+   for (d = 1; d <= K; d++) {
       r *= N--;
       r /= d;
    }
diff --git a/math/math.tex b/math/math.tex
new file mode 100644
index 0000000..e1e0950
--- /dev/null
+++ b/math/math.tex
@@ -0,0 +1,4 @@
+\section{Mathe}
+
+\subsection{Binomialkoeffizienten}
+\lstinputlisting{math/binomial.cpp}
\ No newline at end of file
diff --git a/tcr.pdf b/tcr.pdf
index e5427c3..5116dbf 100644
Binary files a/tcr.pdf and b/tcr.pdf differ
diff --git a/tcr.tex b/tcr.tex
index be50976..be8556d 100644
--- a/tcr.tex
+++ b/tcr.tex
@@ -50,6 +50,7 @@
 \input{datastructures/datastructures}
 \input{graph/graph}
 \input{geometry/geometry}
+\input{math/math}
 \input{sonstiges/sonstiges}
 
 \end{document}
\ No newline at end of file
-- 
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