Merge branch 'master' of github.com:AndreasFMueller/SeminarSpezielleFunktionen

31 files changed, 1152 insertions, 0 deletions

diff --git a/buch/papers/nav/images/position/2k_earth_daymap.png b/buch/papers/nav/images/position/2k_earth_daymap.png
new file mode 100644
index 0000000..4d55da8
--- /dev/null
+++ b/buch/papers/nav/images/position/2k_earth_daymap.png
diff --git a/buch/papers/nav/images/position/Makefile b/buch/papers/nav/images/position/Makefile
new file mode 100644
index 0000000..eed2e56
--- /dev/null
+++ b/buch/papers/nav/images/position/Makefile
@@ -0,0 +1,69 @@
+#
+# Makefile to build images 
+#
+# (c) 2022
+#
+all:	position
+
+POSITION =								\
+	position1.pdf position1-small.pdf				\
+	position2.pdf position2-small.pdf				\
+	position3.pdf position3-small.pdf				\
+	position4.pdf position4-small.pdf				\
+	position5.pdf position5-small.pdf	
+
+position: $(POSITION)
+
+POVRAYOPTIONS = -W1080 -H1080
+#POVRAYOPTIONS = -W480 -H480
+
+position1.png:	position1.pov common.inc ../macros.inc
+	povray +A0.1 $(POVRAYOPTIONS) -Oposition1.png position1.pov
+position1.jpg:	position1.png
+	convert position1.png -density 300 -units PixelsPerInch position1.jpg
+position1.pdf:	position1.tex common.tex position1.jpg
+	pdflatex position1.tex
+
+position2.png:	position2.pov common.inc ../macros.inc
+	povray +A0.1 $(POVRAYOPTIONS) -Oposition2.png position2.pov
+position2.jpg:	position2.png
+	convert position2.png -density 300 -units PixelsPerInch position2.jpg
+position2.pdf:	position2.tex common.tex position2.jpg
+	pdflatex position2.tex
+
+position3.png:	position3.pov common.inc ../macros.inc
+	povray +A0.1 $(POVRAYOPTIONS) -Oposition3.png position3.pov
+position3.jpg:	position3.png
+	convert position3.png -density 300 -units PixelsPerInch position3.jpg
+position3.pdf:	position3.tex common.tex position3.jpg
+	pdflatex position3.tex
+
+position4.png:	position4.pov common.inc ../macros.inc
+	povray +A0.1 $(POVRAYOPTIONS) -Oposition4.png position4.pov
+position4.jpg:	position4.png
+	convert position4.png -density 300 -units PixelsPerInch position4.jpg
+position4.pdf:	position4.tex common.tex position4.jpg
+	pdflatex position4.tex
+
+position5.png:	position5.pov common.inc ../macros.inc
+	povray +A0.1 $(POVRAYOPTIONS) -Oposition5.png position5.pov
+position5.jpg:	position5.png
+	convert position5.png -density 300 -units PixelsPerInch position5.jpg
+position5.pdf:	position5.tex common.tex position5.jpg
+	pdflatex position5.tex
+
+position1-small.pdf:	position1-small.tex common.tex position1.jpg
+	pdflatex position1-small.tex
+position2-small.pdf:	position2-small.tex common.tex position2.jpg
+	pdflatex position2-small.tex
+position3-small.pdf:	position3-small.tex common.tex position3.jpg
+	pdflatex position3-small.tex
+position4-small.pdf:	position4-small.tex common.tex position4.jpg
+	pdflatex position4-small.tex
+position5-small.pdf:	position5-small.tex common.tex position5.jpg
+	pdflatex position5-small.tex
+
+test:	test.pdf
+
+test.pdf:	test.tex $(POSITION)
+	pdflatex test.tex
diff --git a/buch/papers/nav/images/position/common-small.tex b/buch/papers/nav/images/position/common-small.tex
new file mode 100644
index 0000000..9430608
--- /dev/null
+++ b/buch/papers/nav/images/position/common-small.tex
@@ -0,0 +1,32 @@
+%
+% common.tex
+%
+% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+
+\def\labelA{\node at (0.7,3.8) {$A$};}
+\def\labelB{\node at (-3.4,-0.8) {$B$};}
+\def\labelC{\node at (3.3,-2.1) {$C$};}
+\def\labelP{\node at (-1.4,-3.5) {$P$};}
+
+\def\labelc{\node at (-1.9,2.1) {$c$};}
+\def\labela{\node at (-0.2,-1.2) {$a$};}
+\def\labelb{\node at (2.6,1.5) {$b$};}
+
+\def\labelhb{\node at (-2.6,-2.2) {$h_B$};}
+\def\labelhc{\node at (1,-2.9) {$h_C$};}
+\def\labell{\node at (-0.7,0.3) {$l$};}
+
+\def\labelalpha{\node at (0.6,2.85) {$\alpha$};}
+\def\labelbeta{\node at (-2.5,-0.5) {$\beta$};}
+\def\labelgamma{\node at (2.3,-1.2) {$\gamma$};}
+\def\labelomega{\node at (0.85,3.3) {$\omega$};}
+
+\def\labelgammaone{\node at (2.1,-2.0) {$\gamma_1$};}
+\def\labelgammatwo{\node at (2.3,-1.3) {$\gamma_2$};}
+\def\labelbetaone{\node at (-2.4,-1.4) {$\beta_1$};}
+\def\labelbetatwo{\node at (-2.5,-0.8) {$\beta_2$};}
+
+\def\labelomegalinks{\node at (0.25,3.25) {$\omega$};}
+\def\labelomegarechts{\node at (0.85,3.1) {$\omega$};}
+
diff --git a/buch/papers/nav/images/position/common.inc b/buch/papers/nav/images/position/common.inc
new file mode 100644
index 0000000..56e2836
--- /dev/null
+++ b/buch/papers/nav/images/position/common.inc
@@ -0,0 +1,39 @@
+//
+// common.inc -- 3d Darstellung
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+#include "../macros.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.034;
+
+camera {
+	location <40, 20, -20>
+	look_at <0, 0.24, -0.20>
+	right x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<30, 10, -40> color White
+	area_light <1,0,0> <0,0,1>, 10, 10
+	adaptive 1
+	jitter
+}
+
+sky_sphere {
+	pigment {
+		color rgb<1,1,1>
+	}
+}
+
+//kugel(kugeldunkel)
+erde(-100)
+koordinatennetz(gitterfarbe, 9, 0.001)
+achse(fein, White)
diff --git a/buch/papers/nav/images/position/common.tex b/buch/papers/nav/images/position/common.tex
new file mode 100644
index 0000000..9430608
--- /dev/null
+++ b/buch/papers/nav/images/position/common.tex
@@ -0,0 +1,32 @@
+%
+% common.tex
+%
+% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+
+\def\labelA{\node at (0.7,3.8) {$A$};}
+\def\labelB{\node at (-3.4,-0.8) {$B$};}
+\def\labelC{\node at (3.3,-2.1) {$C$};}
+\def\labelP{\node at (-1.4,-3.5) {$P$};}
+
+\def\labelc{\node at (-1.9,2.1) {$c$};}
+\def\labela{\node at (-0.2,-1.2) {$a$};}
+\def\labelb{\node at (2.6,1.5) {$b$};}
+
+\def\labelhb{\node at (-2.6,-2.2) {$h_B$};}
+\def\labelhc{\node at (1,-2.9) {$h_C$};}
+\def\labell{\node at (-0.7,0.3) {$l$};}
+
+\def\labelalpha{\node at (0.6,2.85) {$\alpha$};}
+\def\labelbeta{\node at (-2.5,-0.5) {$\beta$};}
+\def\labelgamma{\node at (2.3,-1.2) {$\gamma$};}
+\def\labelomega{\node at (0.85,3.3) {$\omega$};}
+
+\def\labelgammaone{\node at (2.1,-2.0) {$\gamma_1$};}
+\def\labelgammatwo{\node at (2.3,-1.3) {$\gamma_2$};}
+\def\labelbetaone{\node at (-2.4,-1.4) {$\beta_1$};}
+\def\labelbetatwo{\node at (-2.5,-0.8) {$\beta_2$};}
+
+\def\labelomegalinks{\node at (0.25,3.25) {$\omega$};}
+\def\labelomegarechts{\node at (0.85,3.1) {$\omega$};}
+
diff --git a/buch/papers/nav/images/position/position1-small.pdf b/buch/papers/nav/images/position/position1-small.pdf
new file mode 100644
index 0000000..ba7755f
--- /dev/null
+++ b/buch/papers/nav/images/position/position1-small.pdf
diff --git a/buch/papers/nav/images/position/position1-small.tex b/buch/papers/nav/images/position/position1-small.tex
new file mode 100644
index 0000000..05fad44
--- /dev/null
+++ b/buch/papers/nav/images/position/position1-small.tex
@@ -0,0 +1,55 @@
+%
+% position1-small.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common-small.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.625]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=5cm]{position1.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelC
+\labelP
+
+\labelc
+\labela
+\labelb
+\labell
+
+\labelhb
+\labelhc
+
+\labelalpha
+\labelomega
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position1.pdf b/buch/papers/nav/images/position/position1.pdf
new file mode 100644
index 0000000..fc4f760
--- /dev/null
+++ b/buch/papers/nav/images/position/position1.pdf
diff --git a/buch/papers/nav/images/position/position1.pov b/buch/papers/nav/images/position/position1.pov
new file mode 100644
index 0000000..a79a9f1
--- /dev/null
+++ b/buch/papers/nav/images/position/position1.pov
@@ -0,0 +1,71 @@
+//
+// position1.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "common.inc"
+
+union {
+	seite(B, C, fett)
+	punkt(A, fett)
+	punkt(B, fett)
+	punkt(C, fett)
+	punkt(P, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(A, P, fett)
+	pigment {
+		color rot
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+
+union {
+	seite(A, B, fett)
+	seite(A, C, fett)
+	seite(B, P, fett)
+	seite(C, P, fett)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, B, C, fein, gross)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, P, C, fett, klein)
+	pigment {
+		color rot
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
diff --git a/buch/papers/nav/images/position/position1.tex b/buch/papers/nav/images/position/position1.tex
new file mode 100644
index 0000000..d6c21c3
--- /dev/null
+++ b/buch/papers/nav/images/position/position1.tex
@@ -0,0 +1,55 @@
+%
+% dreieck3d1.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{position1.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelC
+\labelP
+
+\labelc
+\labela
+\labelb
+\labell
+
+\labelhb
+\labelhc
+
+\labelalpha
+\labelomega
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position2-small.pdf b/buch/papers/nav/images/position/position2-small.pdf
new file mode 100644
index 0000000..3333dd4
--- /dev/null
+++ b/buch/papers/nav/images/position/position2-small.pdf
diff --git a/buch/papers/nav/images/position/position2-small.tex b/buch/papers/nav/images/position/position2-small.tex
new file mode 100644
index 0000000..e5c33cf
--- /dev/null
+++ b/buch/papers/nav/images/position/position2-small.tex
@@ -0,0 +1,53 @@
+%
+% position2-small.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common-small.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.625]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=5cm]{position2.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelC
+
+\labelc
+\labela
+\labelb
+
+\begin{scope}[yshift=0.3cm,xshift=0.1cm]
+\labelalpha
+\end{scope}
+\labelbeta
+\labelgamma
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position2.pdf b/buch/papers/nav/images/position/position2.pdf
new file mode 100644
index 0000000..dbd2ea9
--- /dev/null
+++ b/buch/papers/nav/images/position/position2.pdf
diff --git a/buch/papers/nav/images/position/position2.pov b/buch/papers/nav/images/position/position2.pov
new file mode 100644
index 0000000..2abcd94
--- /dev/null
+++ b/buch/papers/nav/images/position/position2.pov
@@ -0,0 +1,70 @@
+//
+// position3.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "common.inc"
+
+dreieck(A, B, C, kugelfarbe)
+
+union {
+	punkt(A, fett)
+	punkt(B, fett)
+	punkt(C, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(A, B, fett)
+	seite(A, C, fett)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(B, C, fett)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, B, C, fein, gross)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	winkel(B, C, A, fein, gross)
+	winkel(C, A, B, fein, gross)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+
diff --git a/buch/papers/nav/images/position/position2.tex b/buch/papers/nav/images/position/position2.tex
new file mode 100644
index 0000000..339592c
--- /dev/null
+++ b/buch/papers/nav/images/position/position2.tex
@@ -0,0 +1,53 @@
+%
+% position2.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{position2.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelC
+
+\labelc
+\labela
+\labelb
+
+\begin{scope}[yshift=0.3cm,xshift=0.1cm]
+\labelalpha
+\end{scope}
+\labelbeta
+\labelgamma
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position3-small.pdf b/buch/papers/nav/images/position/position3-small.pdf
new file mode 100644
index 0000000..fae0b85
--- /dev/null
+++ b/buch/papers/nav/images/position/position3-small.pdf
diff --git a/buch/papers/nav/images/position/position3-small.tex b/buch/papers/nav/images/position/position3-small.tex
new file mode 100644
index 0000000..4f7b0e9
--- /dev/null
+++ b/buch/papers/nav/images/position/position3-small.tex
@@ -0,0 +1,51 @@
+%
+% position3-small.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common-small.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.625]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=5cm]{position3.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelB
+\labelC
+\labelP
+
+\labela
+
+\labelhb
+\labelhc
+
+\labelbetaone
+\labelgammaone
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position3.pdf b/buch/papers/nav/images/position/position3.pdf
new file mode 100644
index 0000000..2c940d2
--- /dev/null
+++ b/buch/papers/nav/images/position/position3.pdf
diff --git a/buch/papers/nav/images/position/position3.pov b/buch/papers/nav/images/position/position3.pov
new file mode 100644
index 0000000..f6823eb
--- /dev/null
+++ b/buch/papers/nav/images/position/position3.pov
@@ -0,0 +1,48 @@
+//
+// position3.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "common.inc"
+
+dreieck(B, P, C, kugelfarbe)
+
+union {
+	punkt(B, fett)
+	punkt(C, fett)
+	punkt(P, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(B, C, fett)
+	seite(B, P, fett)
+	seite(C, P, fett)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	winkel(B, P, C, fein, gross)
+	winkel(C, B, P, fein, gross)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
diff --git a/buch/papers/nav/images/position/position3.tex b/buch/papers/nav/images/position/position3.tex
new file mode 100644
index 0000000..d5480da
--- /dev/null
+++ b/buch/papers/nav/images/position/position3.tex
@@ -0,0 +1,51 @@
+%
+% dreieck3d1.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{position3.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelB
+\labelC
+\labelP
+
+\labela
+
+\labelhb
+\labelhc
+
+\labelbetaone
+\labelgammaone
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position4-small.pdf b/buch/papers/nav/images/position/position4-small.pdf
new file mode 100644
index 0000000..ac80c46
--- /dev/null
+++ b/buch/papers/nav/images/position/position4-small.pdf
diff --git a/buch/papers/nav/images/position/position4-small.tex b/buch/papers/nav/images/position/position4-small.tex
new file mode 100644
index 0000000..e06523b
--- /dev/null
+++ b/buch/papers/nav/images/position/position4-small.tex
@@ -0,0 +1,50 @@
+%
+% position4-small.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common-small.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.625]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=5cm]{position4.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelP
+
+\labelc
+\labell
+\labelhb
+
+\labelomegalinks
+\labelbetatwo
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position4.pdf b/buch/papers/nav/images/position/position4.pdf
new file mode 100644
index 0000000..8eeeaac
--- /dev/null
+++ b/buch/papers/nav/images/position/position4.pdf
diff --git a/buch/papers/nav/images/position/position4.pov b/buch/papers/nav/images/position/position4.pov
new file mode 100644
index 0000000..80628f9
--- /dev/null
+++ b/buch/papers/nav/images/position/position4.pov
@@ -0,0 +1,69 @@
+//
+// position4.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "common.inc"
+
+dreieck(A, B, P, kugelfarbe)
+
+union {
+	punkt(A, fett)
+	punkt(B, fett)
+	punkt(P, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(A, P, fett)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+
+union {
+	seite(A, B, fett)
+	seite(B, P, fett)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(B, P, A, fein, gross)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, B, P, fein, gross)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
diff --git a/buch/papers/nav/images/position/position4.tex b/buch/papers/nav/images/position/position4.tex
new file mode 100644
index 0000000..27c1757
--- /dev/null
+++ b/buch/papers/nav/images/position/position4.tex
@@ -0,0 +1,50 @@
+%
+% position4.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{position4.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelB
+\labelP
+
+\labelc
+\labell
+\labelhb
+
+\labelomegalinks
+\labelbetatwo
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position5-small.pdf b/buch/papers/nav/images/position/position5-small.pdf
new file mode 100644
index 0000000..afe120e
--- /dev/null
+++ b/buch/papers/nav/images/position/position5-small.pdf
diff --git a/buch/papers/nav/images/position/position5-small.tex b/buch/papers/nav/images/position/position5-small.tex
new file mode 100644
index 0000000..0a0e229
--- /dev/null
+++ b/buch/papers/nav/images/position/position5-small.tex
@@ -0,0 +1,50 @@
+%
+% position5-small.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common-small.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.625]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=5cm]{position5.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelC
+\labelP
+
+\labelb
+\labell
+\labelhc
+
+\labelomegarechts
+\labelgammatwo
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/position5.pdf b/buch/papers/nav/images/position/position5.pdf
new file mode 100644
index 0000000..05a64cb
--- /dev/null
+++ b/buch/papers/nav/images/position/position5.pdf
diff --git a/buch/papers/nav/images/position/position5.pov b/buch/papers/nav/images/position/position5.pov
new file mode 100644
index 0000000..7ed33c5
--- /dev/null
+++ b/buch/papers/nav/images/position/position5.pov
@@ -0,0 +1,69 @@
+//
+// position5.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "common.inc"
+
+dreieck(A, P, C, kugelfarbe)
+
+union {
+	punkt(A, fett)
+	punkt(C, fett)
+	punkt(P, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	seite(A, P, fett)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+
+union {
+	seite(A, C, fett)
+	seite(C, P, fett)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(C, P, A, fein, gross)
+	pigment {
+		color bekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, C, P, fein, gross)
+	pigment {
+		color unbekannt
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
diff --git a/buch/papers/nav/images/position/position5.tex b/buch/papers/nav/images/position/position5.tex
new file mode 100644
index 0000000..b234429
--- /dev/null
+++ b/buch/papers/nav/images/position/position5.tex
@@ -0,0 +1,50 @@
+%
+% position5.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\input{common.tex}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{position5.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\labelA
+\labelC
+\labelP
+
+\labelb
+\labell
+\labelhc
+
+\labelomegarechts
+\labelgammatwo
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/position/test.tex b/buch/papers/nav/images/position/test.tex
new file mode 100644
index 0000000..8f4b341
--- /dev/null
+++ b/buch/papers/nav/images/position/test.tex
@@ -0,0 +1,135 @@
+%
+% test.tex
+%
+% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[12pt]{article}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{etex}
+\usepackage[ngerman]{babel}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\usepackage{graphicx}
+\usepackage{wrapfig}
+\begin{document}
+
+\begin{wrapfigure}{R}{5.2cm}
+\includegraphics{position1-small.pdf}
+\end{wrapfigure}
+Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
+Aenean
+commodo ligula eget dolor.
+Aenean massa.
+Cum sociis natoque penatibus
+et magnis dis parturient montes, nascetur ridiculus mus.
+Donec quam
+felis, ultricies nec, pellentesque eu, pretium quis, sem.
+Nulla
+consequat massa quis enim.
+Donec pede justo, fringilla vel, aliquet
+nec, vulputate eget, arcu.
+In enim justo, rhoncus ut, imperdiet a,
+venenatis vitae, justo.
+Nullam dictum felis eu pede mollis pretium.
+Integer tincidunt.
+Cras dapibus.
+Vivamus elementum semper nisi.
+Aenean vulputate eleifend tellus.
+Aenean leo ligula, porttitor eu,
+consequat vitae, eleifend ac, enim.
+Aliquam lorem ante, dapibus in,
+viverra quis, feugiat a, tellus.
+
+\begin{wrapfigure}{R}{5.2cm}
+\includegraphics{position2-small.pdf}
+\end{wrapfigure}
+Maecenas tempus, tellus eget condimentum rhoncus, sem quam semper
+libero, sit amet adipiscing sem neque sed ipsum. Nam quam nunc,
+blandit vel, luctus pulvinar, hendrerit id, lorem. Maecenas nec
+odio et ante tincidunt tempus. Donec vitae sapien ut libero venenatis
+faucibus. Nullam quis ante. Etiam sit amet orci eget eros faucibus
+tincidunt. Duis leo. Sed fringilla mauris sit amet nibh. Donec
+sodales sagittis magna. Sed consequat, leo eget bibendum sodales,
+augue velit cursus nunc, quis gravida magna mi a libero. Fusce
+vulputate eleifend sapien. Vestibulum purus quam, scelerisque ut,
+mollis sed, nonummy id, metus. Nullam accumsan lorem in dui. Cras
+ultricies mi eu turpis hendrerit fringilla. Vestibulum ante ipsum
+primis in faucibus orci luctus et ultrices posuere cubilia Curae;
+
+\pagebreak
+
+\begin{wrapfigure}{R}{5.2cm}
+\includegraphics{position3-small.pdf}
+\end{wrapfigure}
+Integer ante arcu, accumsan a, consectetuer eget, posuere ut, mauris.
+Praesent adipiscing. Phasellus ullamcorper ipsum rutrum nunc. Nunc
+nonummy metus. Vestibulum volutpat pretium libero. Cras id dui.
+Aenean ut eros et nisl sagittis vestibulum. Nullam nulla eros,
+ultricies sit amet, nonummy id, imperdiet feugiat, pede. Sed lectus.
+Donec mollis hendrerit risus. Phasellus nec sem in justo pellentesque
+facilisis. Etiam imperdiet imperdiet orci. Nunc nec neque. Phasellus
+leo dolor, tempus non, auctor et, hendrerit quis, nisi. Curabitur
+ligula sapien, tincidunt non, euismod vitae, posuere imperdiet,
+leo. Maecenas malesuada. Praesent congue erat at massa. Sed cursus
+turpis vitae tortor. Donec posuere vulputate arcu. Phasellus accumsan
+cursus velit. Vestibulum ante ipsum primis in faucibus orci luctus
+et ultrices posuere cubilia Curae; Sed aliquam, nisi quis porttitor
+congue, elit erat euismod orci, ac placerat dolor lectus quis orci.
+Phasellus consectetuer vestibulum elit.
+
+\begin{wrapfigure}{R}{5.2cm}
+\includegraphics{position4-small.pdf}
+\end{wrapfigure}
+Aenean tellus metus, bibendum sed, posuere ac, mattis non, nunc.
+Vestibulum fringilla pede sit amet augue. In turpis. Pellentesque
+posuere. Praesent turpis. Aenean posuere, tortor sed cursus feugiat,
+nunc augue blandit nunc, eu sollicitudin urna dolor sagittis lacus.
+Donec elit libero, sodales nec, volutpat a, suscipit non, turpis.
+Nullam sagittis. Suspendisse pulvinar, augue ac venenatis condimentum,
+sem libero volutpat nibh, nec pellentesque velit pede quis nunc.
+Vestibulum ante ipsum primis in faucibus orci luctus et ultrices
+posuere cubilia Curae; Fusce id purus. Ut varius tincidunt libero.
+Phasellus dolor. Maecenas vestibulum mollis diam. Pellentesque ut
+neque. Pellentesque habitant morbi tristique senectus et netus et
+malesuada fames ac turpis egestas. In dui magna, posuere eget,
+vestibulum et, tempor auctor, justo. In ac felis quis tortor malesuada
+pretium. Pellentesque auctor neque nec urna.
+
+\pagebreak
+
+\begin{wrapfigure}{R}{5.2cm}
+\includegraphics{position5-small.pdf}
+\end{wrapfigure}
+Proin sapien ipsum, porta a, auctor quis, euismod ut, mi. Aenean
+viverra rhoncus pede. Pellentesque habitant morbi tristique senectus
+et netus et malesuada fames ac turpis egestas. Ut non enim eleifend
+felis pretium feugiat. Vivamus quis mi. Phasellus a est. Phasellus
+magna. In hac habitasse platea dictumst. Curabitur at lacus ac velit
+ornare lobortis. Curabitur a felis in nunc fringilla tristique.
+Morbi mattis ullamcorper velit. Phasellus gravida semper nisi.
+Nullam vel sem. Pellentesque libero tortor, tincidunt et, tincidunt
+eget, semper nec, quam. Sed hendrerit. Morbi ac felis. Nunc egestas,
+augue at pellentesque laoreet, felis eros vehicula leo, at malesuada
+velit leo quis pede. Donec interdum, metus et hendrerit aliquet,
+dolor diam sagittis ligula, eget egestas libero turpis vel mi. Nunc
+nulla. Fusce risus nisl, viverra et, tempor et, pretium in, sapien.
+Donec venenatis vulputate lorem. Morbi nec metus. Phasellus blandit
+leo ut odio. Maecenas ullamcorper, dui et placerat feugiat, eros
+pede varius nisi, condimentum viverra felis nunc et lorem. Sed magna
+purus, fermentum eu, tincidunt eu, varius ut, felis. In auctor
+lobortis lacus. Quisque libero metus, condimentum nec, tempor a,
+commodo mollis, magna. Vestibulum ullamcorper mauris at ligula.
+Fusce fermentum. Nullam cursus lacinia erat. Praesent blandit laoreet
+nibh. Fusce convallis metus id felis luctus adipiscing. Pellentesque
+egestas, neque sit amet convallis pulvinar, justo nulla eleifend
+augue, ac auctor orci leo non est. Quisque id mi. Ut tincidunt
+tincidunt erat. Etiam feugiat lorem non metus. Vestibulum dapibus
+nunc ac augue. Curabitur vestibulum aliquam leo. Praesent egestas
+neque eu enim. In hac habitasse platea dictumst. Fusce a quam. Etiam
+ut purus mattis mauris
+
+\end{document}