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-rw-r--r--buch/common/packages.tex1
-rw-r--r--buch/papers/nav/beispiel.txt20
-rw-r--r--buch/papers/nav/images/2k_earth_daymap.pngbin0 -> 1473323 bytes
-rw-r--r--buch/papers/nav/images/Makefile27
-rw-r--r--buch/papers/nav/images/beispiele/2k_earth_daymap.pngbin0 -> 1473323 bytes
-rw-r--r--buch/papers/nav/images/beispiele/Makefile38
-rw-r--r--buch/papers/nav/images/beispiele/beispiele1.pdfbin0 -> 399907 bytes
-rw-r--r--buch/papers/nav/images/beispiele/beispiele1.pov12
-rw-r--r--buch/papers/nav/images/beispiele/beispiele1.tex49
-rw-r--r--buch/papers/nav/images/beispiele/beispiele2.pdfbin0 -> 404679 bytes
-rw-r--r--buch/papers/nav/images/beispiele/beispiele2.pov12
-rw-r--r--buch/papers/nav/images/beispiele/beispiele2.tex50
-rw-r--r--buch/papers/nav/images/beispiele/beispiele3.pdfbin0 -> 401946 bytes
-rw-r--r--buch/papers/nav/images/beispiele/beispiele3.pov12
-rw-r--r--buch/papers/nav/images/beispiele/beispiele3.tex49
-rw-r--r--buch/papers/nav/images/beispiele/common.inc50
-rw-r--r--buch/papers/nav/images/beispiele/common.tex79
-rw-r--r--buch/papers/nav/images/beispiele/geometrie.inc41
-rw-r--r--buch/papers/nav/images/common.inc156
-rw-r--r--buch/papers/nav/images/dreieck3d1.pdfbin90451 -> 85369 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d1.pov3
-rw-r--r--buch/papers/nav/images/dreieck3d10.pov46
-rw-r--r--buch/papers/nav/images/dreieck3d2.pdfbin69523 -> 64256 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d2.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d3.pdfbin82512 -> 77179 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d3.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d4.pdfbin85037 -> 84768 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d4.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d5.pdfbin70045 -> 64209 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d5.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d6.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d7.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d8.jpgbin93432 -> 90015 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d8.pdfbin107370 -> 103952 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d8.pov1
-rw-r--r--buch/papers/nav/images/macros.inc345
-rw-r--r--buch/papers/nav/images/position/2k_earth_daymap.pngbin0 -> 1473323 bytes
-rw-r--r--buch/papers/nav/images/position/Makefile69
-rw-r--r--buch/papers/nav/images/position/common-small.tex32
-rw-r--r--buch/papers/nav/images/position/common.inc39
-rw-r--r--buch/papers/nav/images/position/common.tex32
-rw-r--r--buch/papers/nav/images/position/position1-small.pdfbin0 -> 433626 bytes
-rw-r--r--buch/papers/nav/images/position/position1-small.tex55
-rw-r--r--buch/papers/nav/images/position/position1.pdfbin0 -> 433631 bytes
-rw-r--r--buch/papers/nav/images/position/position1.pov71
-rw-r--r--buch/papers/nav/images/position/position1.tex55
-rw-r--r--buch/papers/nav/images/position/position2-small.pdfbin0 -> 310645 bytes
-rw-r--r--buch/papers/nav/images/position/position2-small.tex53
-rw-r--r--buch/papers/nav/images/position/position2.pdfbin0 -> 310650 bytes
-rw-r--r--buch/papers/nav/images/position/position2.pov70
-rw-r--r--buch/papers/nav/images/position/position2.tex53
-rw-r--r--buch/papers/nav/images/position/position3-small.pdfbin0 -> 417713 bytes
-rw-r--r--buch/papers/nav/images/position/position3-small.tex51
-rw-r--r--buch/papers/nav/images/position/position3.pdfbin0 -> 417714 bytes
-rw-r--r--buch/papers/nav/images/position/position3.pov48
-rw-r--r--buch/papers/nav/images/position/position3.tex51
-rw-r--r--buch/papers/nav/images/position/position4-small.pdfbin0 -> 390331 bytes
-rw-r--r--buch/papers/nav/images/position/position4-small.tex50
-rw-r--r--buch/papers/nav/images/position/position4.pdfbin0 -> 390348 bytes
-rw-r--r--buch/papers/nav/images/position/position4.pov69
-rw-r--r--buch/papers/nav/images/position/position4.tex50
-rw-r--r--buch/papers/nav/images/position/position5-small.pdfbin0 -> 337308 bytes
-rw-r--r--buch/papers/nav/images/position/position5-small.tex50
-rw-r--r--buch/papers/nav/images/position/position5.pdfbin0 -> 337310 bytes
-rw-r--r--buch/papers/nav/images/position/position5.pov69
-rw-r--r--buch/papers/nav/images/position/position5.tex50
-rw-r--r--buch/papers/nav/images/position/test.tex135
67 files changed, 1989 insertions, 166 deletions
diff --git a/buch/common/packages.tex b/buch/common/packages.tex
index 2ab2ad8..eef17c1 100644
--- a/buch/common/packages.tex
+++ b/buch/common/packages.tex
@@ -43,6 +43,7 @@
\usepackage{wasysym}
\usepackage{environ}
\usepackage{appendix}
+\usepackage{wrapfig}
\usepackage{placeins}
\usepackage[all]{xy}
\usetikzlibrary{calc,intersections,through,backgrounds,graphs,positioning,shapes,arrows,fit,math}
diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt
index b8716fc..12c309a 100644
--- a/buch/papers/nav/beispiel.txt
+++ b/buch/papers/nav/beispiel.txt
@@ -5,15 +5,31 @@ Sternzeit: 7h 54m 26.593s 7.90738694h
Deneb
RA 20h 42m 12.14s 20.703372h
-DEC 45 21' 40.3" 45.361194
+DEC 45g 21' 40.3" 45.361194
H 50g 15' 17.1" 50.254750
Azi 59g 36' 02.0" 59.600555
+Altair
+
+RA 19h 51' 53.39" 19.864831h
+DEC 8g 55' 42.3 8.928416
+
+H 45g 27' 48.1" 45.463361
+Azi 117g 16' 14.1" 117.270583
+
+Arktur
+
+RA 14h 16' 42.14" 14.278372
+DEC 19g 03' 47.6 19.063222
+
+H 47g 25' 38.8" 47.427444
+Azi 259g 09' 38.4" 259.160666
+
Spica
RA 13h 26m 23.44s 13.439844h
-DEC -11g 16' 46.8" 11.279666
+DEC -11g 16' 46.8" -11.279666
H 18g 27' 30.0" 18.458333
Azi 240g 23' 52.5" 240.397916
diff --git a/buch/papers/nav/images/2k_earth_daymap.png b/buch/papers/nav/images/2k_earth_daymap.png
new file mode 100644
index 0000000..4d55da8
--- /dev/null
+++ b/buch/papers/nav/images/2k_earth_daymap.png
Binary files differ
diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile
index da4defa..39bfbcf 100644
--- a/buch/papers/nav/images/Makefile
+++ b/buch/papers/nav/images/Makefile
@@ -51,73 +51,80 @@ DREIECKE3D = \
dreieck3d5.pdf \
dreieck3d6.pdf \
dreieck3d7.pdf \
- dreieck3d8.pdf
+ dreieck3d8.pdf
dreiecke3d: $(DREIECKE3D)
POVRAYOPTIONS = -W1080 -H1080
#POVRAYOPTIONS = -W480 -H480
-dreieck3d1.png: dreieck3d1.pov common.inc
+dreieck3d1.png: dreieck3d1.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d1.png dreieck3d1.pov
dreieck3d1.jpg: dreieck3d1.png
convert dreieck3d1.png -density 300 -units PixelsPerInch dreieck3d1.jpg
dreieck3d1.pdf: dreieck3d1.tex dreieck3d1.jpg
pdflatex dreieck3d1.tex
-dreieck3d2.png: dreieck3d2.pov common.inc
+dreieck3d2.png: dreieck3d2.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d2.png dreieck3d2.pov
dreieck3d2.jpg: dreieck3d2.png
convert dreieck3d2.png -density 300 -units PixelsPerInch dreieck3d2.jpg
dreieck3d2.pdf: dreieck3d2.tex dreieck3d2.jpg
pdflatex dreieck3d2.tex
-dreieck3d3.png: dreieck3d3.pov common.inc
+dreieck3d3.png: dreieck3d3.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d3.png dreieck3d3.pov
dreieck3d3.jpg: dreieck3d3.png
convert dreieck3d3.png -density 300 -units PixelsPerInch dreieck3d3.jpg
dreieck3d3.pdf: dreieck3d3.tex dreieck3d3.jpg
pdflatex dreieck3d3.tex
-dreieck3d4.png: dreieck3d4.pov common.inc
+dreieck3d4.png: dreieck3d4.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d4.png dreieck3d4.pov
dreieck3d4.jpg: dreieck3d4.png
convert dreieck3d4.png -density 300 -units PixelsPerInch dreieck3d4.jpg
dreieck3d4.pdf: dreieck3d4.tex dreieck3d4.jpg
pdflatex dreieck3d4.tex
-dreieck3d5.png: dreieck3d5.pov common.inc
+dreieck3d5.png: dreieck3d5.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d5.png dreieck3d5.pov
dreieck3d5.jpg: dreieck3d5.png
convert dreieck3d5.png -density 300 -units PixelsPerInch dreieck3d5.jpg
dreieck3d5.pdf: dreieck3d5.tex dreieck3d5.jpg
pdflatex dreieck3d5.tex
-dreieck3d6.png: dreieck3d6.pov common.inc
+dreieck3d6.png: dreieck3d6.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d6.png dreieck3d6.pov
dreieck3d6.jpg: dreieck3d6.png
convert dreieck3d6.png -density 300 -units PixelsPerInch dreieck3d6.jpg
dreieck3d6.pdf: dreieck3d6.tex dreieck3d6.jpg
pdflatex dreieck3d6.tex
-dreieck3d7.png: dreieck3d7.pov common.inc
+dreieck3d7.png: dreieck3d7.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d7.png dreieck3d7.pov
dreieck3d7.jpg: dreieck3d7.png
convert dreieck3d7.png -density 300 -units PixelsPerInch dreieck3d7.jpg
dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg
pdflatex dreieck3d7.tex
-dreieck3d8.png: dreieck3d8.pov common.inc
+dreieck3d8.png: dreieck3d8.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d8.png dreieck3d8.pov
dreieck3d8.jpg: dreieck3d8.png
convert dreieck3d8.png -density 300 -units PixelsPerInch dreieck3d8.jpg
dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg
pdflatex dreieck3d8.tex
-dreieck3d9.png: dreieck3d9.pov common.inc
+dreieck3d9.png: dreieck3d9.pov common.inc macros.inc
povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d9.png dreieck3d9.pov
dreieck3d9.jpg: dreieck3d9.png
convert dreieck3d9.png -density 300 -units PixelsPerInch dreieck3d9.jpg
dreieck3d9.pdf: dreieck3d9.tex dreieck3d9.jpg
pdflatex dreieck3d9.tex
+dreieck3d10.png: dreieck3d10.pov common.inc macros.inc
+ povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d10.png dreieck3d10.pov
+dreieck3d10.jpg: dreieck3d10.png
+ convert dreieck3d10.png -density 300 -units PixelsPerInch dreieck3d10.jpg
+dreieck3d10.pdf: dreieck3d10.tex dreieck3d10.jpg macros.inc
+ pdflatex dreieck3d10.tex
+
diff --git a/buch/papers/nav/images/beispiele/2k_earth_daymap.png b/buch/papers/nav/images/beispiele/2k_earth_daymap.png
new file mode 100644
index 0000000..4d55da8
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/2k_earth_daymap.png
Binary files differ
diff --git a/buch/papers/nav/images/beispiele/Makefile b/buch/papers/nav/images/beispiele/Makefile
new file mode 100644
index 0000000..9546c8e
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/Makefile
@@ -0,0 +1,38 @@
+#
+# Makefile to build images
+#
+# (c) 2022
+#
+all: beispiele
+
+POSITION = \
+ beispiele1.pdf \
+ beispiele2.pdf \
+ beispiele3.pdf
+
+beispiele: $(POSITION)
+
+POVRAYOPTIONS = -W1080 -H1080
+#POVRAYOPTIONS = -W480 -H480
+
+beispiele1.png: beispiele1.pov common.inc geometrie.inc ../macros.inc
+ povray +A0.1 $(POVRAYOPTIONS) -Obeispiele1.png beispiele1.pov
+beispiele1.jpg: beispiele1.png
+ convert beispiele1.png -density 300 -units PixelsPerInch beispiele1.jpg
+beispiele1.pdf: beispiele1.tex common.tex beispiele1.jpg
+ pdflatex beispiele1.tex
+
+beispiele2.png: beispiele2.pov common.inc geometrie.inc ../macros.inc
+ povray +A0.1 $(POVRAYOPTIONS) -Obeispiele2.png beispiele2.pov
+beispiele2.jpg: beispiele2.png
+ convert beispiele2.png -density 300 -units PixelsPerInch beispiele2.jpg
+beispiele2.pdf: beispiele2.tex common.tex beispiele2.jpg
+ pdflatex beispiele2.tex
+
+beispiele3.png: beispiele3.pov common.inc geometrie.inc ../macros.inc
+ povray +A0.1 $(POVRAYOPTIONS) -Obeispiele3.png beispiele3.pov
+beispiele3.jpg: beispiele3.png
+ convert beispiele3.png -density 300 -units PixelsPerInch beispiele3.jpg
+beispiele3.pdf: beispiele3.tex common.tex beispiele3.jpg
+ pdflatex beispiele3.tex
+
diff --git a/buch/papers/nav/images/beispiele/beispiele1.pdf b/buch/papers/nav/images/beispiele/beispiele1.pdf
new file mode 100644
index 0000000..d0fe3dc
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele1.pdf
Binary files differ
diff --git a/buch/papers/nav/images/beispiele/beispiele1.pov b/buch/papers/nav/images/beispiele/beispiele1.pov
new file mode 100644
index 0000000..7fb3de2
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele1.pov
@@ -0,0 +1,12 @@
+//
+// beispiele1.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+#declare Stern1 = Deneb;
+#declare Stern2 = Arktur;
+
+#include "geometrie.inc"
+
diff --git a/buch/papers/nav/images/beispiele/beispiele1.tex b/buch/papers/nav/images/beispiele/beispiele1.tex
new file mode 100644
index 0000000..5666ba6
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele1.tex
@@ -0,0 +1,49 @@
+%
+% beispiele1.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,calc}
+\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]{beispiele1.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
+\labelP
+\labelDeneb
+\labelArktur
+\labelhDeneb
+\labelhArktur
+\labellone
+\labeldDeneb
+\labeldArktur
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/beispiele/beispiele2.pdf b/buch/papers/nav/images/beispiele/beispiele2.pdf
new file mode 100644
index 0000000..8579ee5
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele2.pdf
Binary files differ
diff --git a/buch/papers/nav/images/beispiele/beispiele2.pov b/buch/papers/nav/images/beispiele/beispiele2.pov
new file mode 100644
index 0000000..b69f0f9
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele2.pov
@@ -0,0 +1,12 @@
+//
+// beispiele1.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+#declare Stern1 = Altair;
+#declare Stern2 = Spica;
+
+#include "geometrie.inc"
+
diff --git a/buch/papers/nav/images/beispiele/beispiele2.tex b/buch/papers/nav/images/beispiele/beispiele2.tex
new file mode 100644
index 0000000..c9b70bd
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele2.tex
@@ -0,0 +1,50 @@
+%
+% beispiele2.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,calc}
+\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]{beispiele2.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
+\labelP
+\labelAltair
+\labelSpica
+\labelhAltair
+\labelhSpica
+\labelltwo
+\labeldAltair
+\labeldSpica
+
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/beispiele/beispiele3.pdf b/buch/papers/nav/images/beispiele/beispiele3.pdf
new file mode 100644
index 0000000..a7189dd
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele3.pdf
Binary files differ
diff --git a/buch/papers/nav/images/beispiele/beispiele3.pov b/buch/papers/nav/images/beispiele/beispiele3.pov
new file mode 100644
index 0000000..af9a468
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele3.pov
@@ -0,0 +1,12 @@
+//
+// beispiele1.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+#declare Stern1 = Deneb;
+#declare Stern2 = Altair;
+
+#include "geometrie.inc"
+
diff --git a/buch/papers/nav/images/beispiele/beispiele3.tex b/buch/papers/nav/images/beispiele/beispiele3.tex
new file mode 100644
index 0000000..2573199
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/beispiele3.tex
@@ -0,0 +1,49 @@
+%
+% beispiele3.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,calc}
+\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]{beispiele3.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
+\labelP
+\labelDeneb
+\labelAltair
+\labelhDeneb
+\labelhAltair
+\labellone
+%\labeldDeneb
+%\labeldAltair
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/nav/images/beispiele/common.inc b/buch/papers/nav/images/beispiele/common.inc
new file mode 100644
index 0000000..51fbd1f
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/common.inc
@@ -0,0 +1,50 @@
+//
+// 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>
+ }
+}
+
+erde(0)
+achse(fein, White)
+koordinatennetz(gitterfarbe, 9, 0.001)
+
+union {
+ punkt(Sakura, fett)
+ pigment {
+ color rot
+ }
+ finish {
+ metallic
+ specular 0.9
+ }
+}
+
diff --git a/buch/papers/nav/images/beispiele/common.tex b/buch/papers/nav/images/beispiele/common.tex
new file mode 100644
index 0000000..b7b3dac
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/common.tex
@@ -0,0 +1,79 @@
+%
+% common.tex
+%
+% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+
+\def\labelA{\node at (0.7,3.8) {$A$};}
+
+\def\labelSpica{
+ \node at (-3.6,-2.8) {Spica};
+}
+\def\labelAltair{
+ \node at (3.0,-2.3) {Altair};
+}
+\def\labelArktur{
+ \node at (-3.3,-0.7) {Arktur};
+}
+\def\labelDeneb{
+ \node at (3.4,0.9) {Deneb};
+}
+
+\def\labelP{\node at (0,-0.2) {$P$};}
+
+\def\labellone{\node at (0.1,1.9) {$l$};}
+\def\labelltwo{\node at (0.1,2.0) {$l$};}
+
+\def\labelhSpica{
+ \coordinate (Spica) at (-1.8,-0.3);
+ \node at (Spica) {$h_{\text{Spica}}\mathstrut$};
+}
+\def\labelhAltair{
+ \coordinate (Altair) at (1.1,-1.0);
+ \node at (Altair) {$h_{\text{Altair}}\mathstrut$};
+}
+\def\labelhArktur{
+ \coordinate (Arktur) at (-1.3,-0.3);
+ \node at (Arktur) {$h_{\text{Arktur}}\mathstrut$};
+}
+\def\labelhDeneb{
+ \coordinate (Deneb) at (1.6,0.45);
+ \node at (Deneb) {$h_{\text{Deneb}}\mathstrut$};
+}
+
+\def\labeldSpica{
+ \coordinate (dSpica) at (-1.5,2.6);
+ \fill[color=white,opacity=0.5]
+ ($(dSpica)+(-1.8,0.08)$)
+ rectangle
+ ($(dSpica)+(-0.06,0.55)$);
+ \node at (dSpica) [above left]
+ {$90^\circ-\delta_{\text{Spica}}\mathstrut$};
+}
+\def\labeldAltair{
+ \coordinate (dAltair) at (2.0,2.1);
+ \fill[color=white,opacity=0.5]
+ ($(dAltair)+(0.10,0.05)$)
+ rectangle
+ ($(dAltair)+(1.8,0.5)$);
+ \node at (dAltair) [above right]
+ {$90^\circ-\delta_{\text{Altair}}\mathstrut$};
+}
+\def\labeldArktur{
+ \coordinate (dArktur) at (-1.2,2.5);
+ \fill[color=white,opacity=0.5]
+ ($(dArktur)+(-1.8,0.05)$)
+ rectangle
+ ($(dArktur)+(-0.06,0.5)$);
+ \node at (dArktur) [above left]
+ {$90^\circ-\delta_{\text{Arktur}}\mathstrut$};
+}
+\def\labeldDeneb{
+ \coordinate (dDeneb) at (2.0,2.8);
+ \fill[color=white,opacity=0.5]
+ ($(dDeneb)+(0.05,0.5)$)
+ rectangle
+ ($(dDeneb)+(1.87,0.05)$);
+ \node at (dDeneb) [above right]
+ {$90^\circ-\delta_{\text{Deneb}}\mathstrut$};
+}
diff --git a/buch/papers/nav/images/beispiele/geometrie.inc b/buch/papers/nav/images/beispiele/geometrie.inc
new file mode 100644
index 0000000..2f6084e
--- /dev/null
+++ b/buch/papers/nav/images/beispiele/geometrie.inc
@@ -0,0 +1,41 @@
+union {
+ punkt(A, fett)
+ punkt(Stern1, fein)
+ punkt(Stern2, fein)
+ seite(Stern1, Stern2, fein)
+ pigment {
+ color kugelfarbe
+ }
+ finish {
+ metallic
+ specular 0.9
+ }
+}
+
+union {
+ seite(A, Stern1, fein)
+ seite(A, Stern2, fein)
+ seite(Stern1, Sakura, fein)
+ seite(Stern2, Sakura, fein)
+ winkel(A, Stern1, Stern2, 0.5*fein, gross)
+ pigment {
+ color bekannt
+ }
+ finish {
+ metallic
+ specular 0.9
+ }
+}
+
+union {
+ seite(A, Sakura, fein)
+ winkel(A, Sakura, Stern1, 0.5*fett, klein)
+ pigment {
+ color unbekannt
+ }
+ finish {
+ metallic
+ specular 0.9
+ }
+}
+
diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc
index 2c0ae6e..7b861de 100644
--- a/buch/papers/nav/images/common.inc
+++ b/buch/papers/nav/images/common.inc
@@ -5,6 +5,7 @@
//
#version 3.7;
#include "colors.inc"
+#include "macros.inc"
global_settings {
assumed_gamma 1
@@ -12,12 +13,6 @@ global_settings {
#declare imagescale = 0.034;
-#declare O = <0, 0, 0>;
-#declare A = vnormalize(< 0, 1, 0>);
-#declare B = vnormalize(< 1, 2, -8>);
-#declare C = vnormalize(< 5, 1, 0>);
-#declare P = vnormalize(< 5, -1, -7>);
-
camera {
location <40, 20, -20>
look_at <0, 0.24, -0.20>
@@ -26,7 +21,7 @@ camera {
}
light_source {
- <10, 10, -40> color White
+ <30, 10, -40> color White
area_light <1,0,0> <0,0,1>, 10, 10
adaptive 1
jitter
@@ -38,150 +33,3 @@ sky_sphere {
}
}
-//
-// draw an arrow from <from> to <to> with thickness <arrowthickness> with
-// color <c>
-//
-#macro arrow(from, to, arrowthickness, c)
-#declare arrowdirection = vnormalize(to - from);
-#declare arrowlength = vlength(to - from);
-union {
- sphere {
- from, 1.1 * arrowthickness
- }
- cylinder {
- from,
- from + (arrowlength - 5 * arrowthickness) * arrowdirection,
- arrowthickness
- }
- cone {
- from + (arrowlength - 5 * arrowthickness) * arrowdirection,
- 2 * arrowthickness,
- to,
- 0
- }
- pigment {
- color c
- }
- finish {
- specular 0.9
- metallic
- }
-}
-#end
-
-#macro grosskreis(normale, staerke)
-union {
- #declare v1 = vcross(normale, <normale.x, normale.z, normale.y>);
- #declare v1 = vnormalize(v1);
- #declare v2 = vnormalize(vcross(v1, normale));
- #declare phisteps = 100;
- #declare phistep = pi / phisteps;
- #declare phi = 0;
- #declare p1 = v1;
- #while (phi < 2 * pi - phistep/2)
- sphere { p1, staerke }
- #declare phi = phi + phistep;
- #declare p2 = v1 * cos(phi) + v2 * sin(phi);
- cylinder { p1, p2, staerke }
- #declare p1 = p2;
- #end
-}
-#end
-
-#macro seite(p, q, staerke)
- #declare n = vcross(p, q);
- intersection {
- grosskreis(n, staerke)
- plane { -vcross(n, q) * vdot(vcross(n, q), p), 0 }
- plane { -vcross(n, p) * vdot(vcross(n, p), q), 0 }
- }
-#end
-
-#macro winkel(w, p, q, staerke, r)
- #declare n = vnormalize(w);
- #declare pp = vnormalize(p - vdot(n, p) * n);
- #declare qq = vnormalize(q - vdot(n, q) * n);
- intersection {
- sphere { O, 1 + staerke }
- cone { O, 0, 1.2 * vnormalize(w), r }
- plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 }
- plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 }
- }
-#end
-
-#macro punkt(p, staerke)
- sphere { p, 1.5 * staerke }
-#end
-
-#macro dreieck(p, q, r, farbe)
- #declare n1 = vnormalize(vcross(p, q));
- #declare n2 = vnormalize(vcross(q, r));
- #declare n3 = vnormalize(vcross(r, p));
- intersection {
- plane { n1, 0 }
- plane { n2, 0 }
- plane { n3, 0 }
- sphere { <0, 0, 0>, 1 + 0.001 }
- pigment {
- color farbe
- }
- finish {
- metallic
- specular 0.4
- }
- }
-#end
-
-#macro ebenerwinkel(a, p, q, s, r, farbe)
- #declare n = vnormalize(-vcross(p, q));
- #declare np = vnormalize(-vcross(p, n));
- #declare nq = -vnormalize(-vcross(q, n));
-// arrow(a, a + n, 0.02, White)
-// arrow(a, a + np, 0.01, Red)
-// arrow(a, a + nq, 0.01, Blue)
- intersection {
- cylinder { a - (s/2) * n, a + (s/2) * n, r }
- plane { np, vdot(np, a) }
- plane { nq, vdot(nq, a) }
- pigment {
- farbe
- }
- finish {
- metallic
- specular 0.5
- }
- }
-#end
-
-#macro komplement(a, p, q, s, r, farbe)
- #declare n = vnormalize(-vcross(p, q));
-// arrow(a, a + n, 0.015, Orange)
- #declare m = vnormalize(-vcross(q, n));
-// arrow(a, a + m, 0.015, Pink)
- ebenerwinkel(a, p, m, s, r, farbe)
-#end
-
-#declare fett = 0.015;
-#declare fein = 0.010;
-
-#declare klein = 0.3;
-#declare gross = 0.4;
-
-#declare dreieckfarbe = rgb<0.6,0.6,0.6>;
-#declare rot = rgb<0.8,0.2,0.2>;
-#declare gruen = rgb<0,0.6,0>;
-#declare blau = rgb<0.2,0.2,0.8>;
-
-#declare kugelfarbe = rgb<0.8,0.8,0.8>;
-#declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>;
-
-#macro kugel(farbe)
-sphere {
- <0, 0, 0>, 1
- pigment {
- color farbe
- }
-}
-#end
-
diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf
index 015bce7..fecaece 100644
--- a/buch/papers/nav/images/dreieck3d1.pdf
+++ b/buch/papers/nav/images/dreieck3d1.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov
index e491075..336161c 100644
--- a/buch/papers/nav/images/dreieck3d1.pov
+++ b/buch/papers/nav/images/dreieck3d1.pov
@@ -3,8 +3,11 @@
//
// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
//
+#version 3.7;
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, B, fett)
seite(B, C, fett)
diff --git a/buch/papers/nav/images/dreieck3d10.pov b/buch/papers/nav/images/dreieck3d10.pov
new file mode 100644
index 0000000..2dd7c79
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d10.pov
@@ -0,0 +1,46 @@
+//
+// dreiecke3d10.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+erde()
+
+#declare Stern1 = Deneb;
+#declare Stern2 = Spica;
+
+koordinatennetz(gitterfarbe, 9, 0.001)
+
+union {
+ seite(A, Stern1, 0.5*fein)
+ seite(A, Stern2, 0.5*fein)
+ seite(A, Sakura, 0.5*fein)
+ seite(Stern1, Sakura, 0.5*fein)
+ seite(Stern2, Sakura, 0.5*fein)
+ seite(Stern1, Stern2, 0.5*fein)
+
+ punkt(A, fein)
+ punkt(Sakura, fett)
+ punkt(Deneb, fein)
+ punkt(Spica, fein)
+ punkt(Altair, fein)
+ punkt(Arktur, fein)
+ pigment {
+ color Red
+ }
+}
+
+//arrow(<-1.3,0,0>, <1.3,0,0>, fein, White)
+arrow(<0,-1.3,0>, <0,1.3,0>, fein, White)
+//arrow(<0,0,-1.3>, <0,0,1.3>, fein, White)
+
+#declare imagescale = 0.044;
+
+camera {
+ location <40, 20, -20>
+ look_at <0, 0.24, -0.20>
+ right x * imagescale
+ up y * imagescale
+}
+
diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf
index 6b3f09d..28af5fe 100644
--- a/buch/papers/nav/images/dreieck3d2.pdf
+++ b/buch/papers/nav/images/dreieck3d2.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov
index c0625ce..9e57d22 100644
--- a/buch/papers/nav/images/dreieck3d2.pov
+++ b/buch/papers/nav/images/dreieck3d2.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, B, fett)
seite(B, C, fett)
diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf
index 7d79455..4fc4fc1 100644
--- a/buch/papers/nav/images/dreieck3d3.pdf
+++ b/buch/papers/nav/images/dreieck3d3.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov
index b6f64d5..bde780b 100644
--- a/buch/papers/nav/images/dreieck3d3.pov
+++ b/buch/papers/nav/images/dreieck3d3.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, B, fett)
seite(B, C, fett)
diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf
index e1ea757..0d57fc2 100644
--- a/buch/papers/nav/images/dreieck3d4.pdf
+++ b/buch/papers/nav/images/dreieck3d4.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov
index b6f17e3..08f266b 100644
--- a/buch/papers/nav/images/dreieck3d4.pov
+++ b/buch/papers/nav/images/dreieck3d4.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugelfarbe)
+
union {
seite(A, B, fein)
seite(A, C, fein)
diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf
index 0c86d36..a5dd0ae 100644
--- a/buch/papers/nav/images/dreieck3d5.pdf
+++ b/buch/papers/nav/images/dreieck3d5.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov
index 188f181..1aac0dc 100644
--- a/buch/papers/nav/images/dreieck3d5.pov
+++ b/buch/papers/nav/images/dreieck3d5.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, B, fein)
seite(A, C, fein)
diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov
index 191a1e7..6bbd1a9 100644
--- a/buch/papers/nav/images/dreieck3d6.pov
+++ b/buch/papers/nav/images/dreieck3d6.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, B, fett)
seite(A, C, fett)
diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov
index aae5c6c..45dc5d6 100644
--- a/buch/papers/nav/images/dreieck3d7.pov
+++ b/buch/papers/nav/images/dreieck3d7.pov
@@ -5,6 +5,8 @@
//
#include "common.inc"
+kugel(kugeldunkel)
+
union {
seite(A, C, fett)
seite(A, P, fett)
diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg
index 52bd25e..f24ea33 100644
--- a/buch/papers/nav/images/dreieck3d8.jpg
+++ b/buch/papers/nav/images/dreieck3d8.jpg
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf
index 9d630aa..da3b110 100644
--- a/buch/papers/nav/images/dreieck3d8.pdf
+++ b/buch/papers/nav/images/dreieck3d8.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov
index 9e9921a..dae7f67 100644
--- a/buch/papers/nav/images/dreieck3d8.pov
+++ b/buch/papers/nav/images/dreieck3d8.pov
@@ -93,4 +93,5 @@ object {
dreieck(A, B, C, White)
+kugel(kugeldunkel)
diff --git a/buch/papers/nav/images/macros.inc b/buch/papers/nav/images/macros.inc
new file mode 100644
index 0000000..20cb2ff
--- /dev/null
+++ b/buch/papers/nav/images/macros.inc
@@ -0,0 +1,345 @@
+//
+// macros.inc -- 3d Darstellung
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+//
+// Dimensions
+//
+#declare fett = 0.015;
+#declare fein = 0.010;
+
+#declare klein = 0.3;
+#declare gross = 0.4;
+
+//
+// colors
+//
+#declare dreieckfarbe = rgb<0.6,0.6,0.6>;
+#declare rot = rgb<0.8,0.2,0.2>;
+#declare gruen = rgb<0,0.6,0>;
+#declare blau = rgb<0.2,0.2,0.8>;
+
+#declare bekannt = rgb<0.2,0.6,1>;
+#declare unbekannt = rgb<1.0,0.6,0.8>;
+
+#declare kugelfarbe = rgb<0.8,0.8,0.8>;
+#declare kugeldunkel = rgb<0.4,0.4,0.4>;
+#declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>;
+
+#declare gitterfarbe = rgb<0.2,0.6,1>;
+#declare gitterfarbe = rgb<1.0,0.8,0>;
+
+//
+// Points Points
+//
+#declare O = <0, 0, 0>;
+#declare Nordpol = vnormalize(< 0, 1, 0>);
+#declare A = vnormalize(< 0, 1, 0>);
+#declare B = vnormalize(< 1, 2, -8>);
+#declare C = vnormalize(< 5, 1, 0>);
+#declare P = vnormalize(< 5, -1, -7>);
+
+//
+// \brief convert spherical coordinates to recctangular coordinates
+//
+// \param phi
+// \param theta
+//
+#macro kugelpunkt(phi, theta)
+ < sin(theta) * cos(phi - pi), cos(theta), sin(theta) * sin(phi - pi) >
+#end
+
+#declare Sakura = kugelpunkt(radians(140.2325498), radians(90 - 35.71548014));
+#declare Deneb = kugelpunkt(radians(191.9397759), radians(90 - 45.361194));
+#declare Spica = kugelpunkt(radians(82.9868559), radians(90 - (-11.279666)));
+#declare Altair = kugelpunkt(radians(179.3616609), radians(90 - 8.928416));
+#declare Arktur = kugelpunkt(radians(95.5647759), radians(90 - 19.063222));
+
+//
+// draw an arrow from <from> to <to> with thickness <arrowthickness> with
+// color <c>
+//
+#macro arrow(from, to, arrowthickness, c)
+#declare arrowdirection = vnormalize(to - from);
+#declare arrowlength = vlength(to - from);
+union {
+ sphere {
+ from, 1.1 * arrowthickness
+ }
+ cylinder {
+ from,
+ from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+ arrowthickness
+ }
+ cone {
+ from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+ 2 * arrowthickness,
+ to,
+ 0
+ }
+ pigment {
+ color c
+ }
+ finish {
+ specular 0.9
+ metallic
+ }
+}
+#end
+
+#declare ntsteps = 100;
+
+//
+// \brief Draw a circle
+//
+// \param b1 basis vector for a coordinate system of the plane containing
+// the circle
+// \param b2 the other basis vector
+// \param o center of the circle
+// \param thick diameter of the circular tube
+//
+#macro kreis(b1, b2, o, thick, maxwinkel)
+ #declare tpstep = pi / ntsteps;
+ #declare tp = tpstep;
+ #declare p1 = b1 + o;
+ sphere { p1, thick }
+ #declare tpstep = pi/ntsteps;
+ #while (tp < (maxwinkel - tpstep/2))
+ #declare p2 = cos(tp) * b1 + sin(tp) * b2 + o;
+ cylinder { p1, p2, thick }
+ sphere { p2, thick }
+ #declare p1 = p2;
+ #declare tp = tp + tpstep;
+ #end
+ #if ((tp - tpstep) < maxwinkel)
+ #declare p2 = cos(maxwinkel) * b1 + sin(maxwinkel) * b2 + o;
+ cylinder { p1, p2, thick }
+ sphere { p2, thick }
+ #end
+#end
+
+//
+// \brief Draw a great circle
+//
+// \param normale the normal of the plane containing the great circle
+// \param thick diameter
+//
+#macro grosskreis(normale, thick)
+ #declare other = < normale.y, -normale.x, normale.z >;
+ #declare b1 = vnormalize(vcross(other, normale));
+ #declare b2 = vnormalize(vcross(normale, b1));
+ kreis(b1, b2, <0,0,0>, thick, 2*pi)
+#end
+
+//
+// \brief Draw a circle of latitude
+//
+// \param theta latitude
+// \param thick diameter
+//
+#macro breitenkreis(theta, thick)
+ #declare b1 = sin(theta) * kugelpunkt(0, pi/2);
+ #declare b2 = sin(theta) * kugelpunkt(pi/2, pi/2);
+ #declare o = < 0, cos(theta), 0 >;
+ kreis(b1, b2, o, thick, 2*pi)
+#end
+
+//
+// \brief Draw the great circle connecting the two points
+//
+// \param p first point
+// \param q second point
+// \param staerke diameter
+//
+
+#macro seite(p, q, staerke)
+ #declare s1 = vnormalize(p);
+ #declare s2 = vnormalize(q);
+ #declare w = acos(vdot(s1, s2));
+ #declare n = vnormalize(vcross(p, q));
+ #declare s2 = vnormalize(vcross(n, s1));
+ kreis(s1, s2, O, staerke, w)
+#end
+
+//
+// \brief Draw an angle
+//
+// \param w the edge where the angle is located
+// \param p point on the first leg
+// \param q point on the second leg
+// \param r diameter of the angle
+//
+#macro winkel(w, p, q, staerke, r)
+ #declare n = vnormalize(w);
+ #declare pp = vnormalize(p - vdot(n, p) * n);
+ #declare qq = vnormalize(q - vdot(n, q) * n);
+ intersection {
+ sphere { O, 1 + staerke }
+ cone { O, 0, 1.2 * vnormalize(w), r }
+ plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 }
+ plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 }
+ }
+#end
+
+//
+// \brief Draw a point on the sphere as a circle
+//
+// \param p the point
+// \param staerke the diameter of the point
+//
+#macro punkt(p, staerke)
+ sphere { p, 1.5 * staerke }
+#end
+
+//
+// \brief Draw a circle as a part of the differently colored cutout from
+// the sphere
+//
+// \param p first point of the triangle
+// \param q second point of the triangle
+// \param r third point of the triangle
+// \param farbe color
+//
+#macro dreieck(p, q, r, farbe)
+ #declare n1 = vnormalize(vcross(p, q));
+ #declare n2 = vnormalize(vcross(q, r));
+ #declare n3 = vnormalize(vcross(r, p));
+ intersection {
+ plane { n1, 0 }
+ plane { n2, 0 }
+ plane { n3, 0 }
+ sphere { <0, 0, 0>, 1 + 0.001 }
+ pigment {
+ color farbe
+ }
+ finish {
+ metallic
+ specular 0.4
+ }
+ }
+#end
+
+//
+// \brief
+//
+// \param a axis of the angle
+// \param p first leg
+// \param q second leg
+// \param s thickness of the angle disk
+// \param r radius of the angle disk
+// \param farbe color
+//
+#macro ebenerwinkel(a, p, q, s, r, farbe)
+ #declare n = vnormalize(-vcross(p, q));
+ #declare np = vnormalize(-vcross(p, n));
+ #declare nq = -vnormalize(-vcross(q, n));
+// arrow(a, a + n, 0.02, White)
+// arrow(a, a + np, 0.01, Red)
+// arrow(a, a + nq, 0.01, Blue)
+ intersection {
+ cylinder { a - (s/2) * n, a + (s/2) * n, r }
+ plane { np, vdot(np, a) }
+ plane { nq, vdot(nq, a) }
+ pigment {
+ farbe
+ }
+ finish {
+ metallic
+ specular 0.5
+ }
+ }
+#end
+
+//
+// \brief Show the complement angle
+//
+//
+#macro komplement(a, p, q, s, r, farbe)
+ #declare n = vnormalize(-vcross(p, q));
+// arrow(a, a + n, 0.015, Orange)
+ #declare m = vnormalize(-vcross(q, n));
+// arrow(a, a + m, 0.015, Pink)
+ ebenerwinkel(a, p, m, s, r, farbe)
+#end
+
+//
+// \brief Show a coordinate grid on the sphere
+//
+// \param farbe the color of the grid
+// \param thick the line thickness
+//
+#macro koordinatennetz(farbe, netzschritte, thick)
+union {
+ // circles of latitude
+ #declare theta = pi/(2*netzschritte);
+ #declare thetastep = pi/(2*netzschritte);
+ #while (theta < pi - thetastep/2)
+ breitenkreis(theta, thick)
+ #declare theta = theta + thetastep;
+ #end
+ // cirles of longitude
+ #declare phi = 0;
+ #declare phistep = pi/(2*netzschritte);
+ #while (phi < pi-phistep/2)
+ grosskreis(kugelpunkt(phi, pi/2), thick)
+ #declare phi = phi + phistep;
+ #end
+ pigment {
+ color farbe
+ }
+ finish {
+ specular 0.9
+ metallic
+ }
+}
+#end
+
+//
+// \brief Display a color of given color
+//
+// \param farbe the color
+//
+#macro kugel(farbe)
+sphere {
+ <0, 0, 0>, 1
+ pigment {
+ color farbe
+ }
+}
+#end
+
+//
+// \brief Display the earth
+//
+#macro erde(winkel)
+sphere {
+ <0, 0, 0>, 1
+ pigment {
+ image_map {
+ png "2k_earth_daymap.png" gamma 1.0
+ map_type 1
+ }
+ }
+ rotate <0,winkel,0>
+}
+#end
+
+//
+// achse
+//
+#macro achse(durchmesser, farbe)
+ cylinder {
+ < 0, -1.2, 0 >, <0, 1.2, 0 >, durchmesser
+ pigment {
+ color farbe
+ }
+ finish {
+ specular 0.9
+ metallic
+ }
+ }
+#end
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
+
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+Proin sapien ipsum, porta a, auctor quis, euismod ut, mi. Aenean
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+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.
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+leo ut odio. Maecenas ullamcorper, dui et placerat feugiat, eros
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+commodo mollis, magna. Vestibulum ullamcorper mauris at ligula.
+Fusce fermentum. Nullam cursus lacinia erat. Praesent blandit laoreet
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+egestas, neque sit amet convallis pulvinar, justo nulla eleifend
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+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}