add position subdirectory

36 files changed, 1087 insertions, 164 deletions

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/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
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/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
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
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
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
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
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
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..2def6fd
--- /dev/null
+++ b/buch/papers/nav/images/macros.inc
@@ -0,0 +1,343 @@
+//
+// 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>;
+
+//
+// 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()
+sphere {
+	<0, 0, 0>, 1
+	pigment {
+		image_map {
+			png "2k_earth_daymap.png" gamma 1.0
+			map_type 1
+		}
+	}
+}
+#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/Makefile b/buch/papers/nav/images/position/Makefile
new file mode 100644
index 0000000..280e59c
--- /dev/null
+++ b/buch/papers/nav/images/position/Makefile
@@ -0,0 +1,54 @@
+#
+# Makefile to build images 
+#
+# (c) 2022
+#
+all:	position
+
+POSITION =								\
+	position1.pdf							\
+	position2.pdf							\
+	position3.pdf							\
+	position4.pdf							\
+	position5.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 $(POVRAYOPTIONS) -Oposition5.png position5.pov
+position5.jpg:	position5.png
+	convert position5.png -density 300 -units PixelsPerInch position5.jpg
+position5.pdf:	position5.tex common.tex position5.jpg
+	pdflatex position5.tex
+
diff --git a/buch/papers/nav/images/position/common.inc b/buch/papers/nav/images/position/common.inc
new file mode 100644
index 0000000..b50b8d6
--- /dev/null
+++ b/buch/papers/nav/images/position/common.inc
@@ -0,0 +1,37 @@
+//
+// common.inc -- 3d Darstellung
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+#include "../macros.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.034;
+
+camera {
+	location <40, 20, -20>
+	look_at <0, 0.24, -0.20>
+	right x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<30, 10, -40> color White
+	area_light <1,0,0> <0,0,1>, 10, 10
+	adaptive 1
+	jitter
+}
+
+sky_sphere {
+	pigment {
+		color rgb<1,1,1>
+	}
+}
+
+kugel(kugeldunkel)
+achse(fein, White)
diff --git a/buch/papers/nav/images/position/common.tex b/buch/papers/nav/images/position/common.tex
new file mode 100644
index 0000000..d72a981
--- /dev/null
+++ b/buch/papers/nav/images/position/common.tex
@@ -0,0 +1,32 @@
+%
+% common.tex
+%
+% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+
+\def\labelA{\node at (0.7,3.8) {$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.pdf b/buch/papers/nav/images/position/position1.pdf
new file mode 100644
index 0000000..1bd9a69
--- /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.pdf b/buch/papers/nav/images/position/position2.pdf
new file mode 100644
index 0000000..6015ba1
--- /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.pdf b/buch/papers/nav/images/position/position3.pdf
new file mode 100644
index 0000000..dea8c28
--- /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.pdf b/buch/papers/nav/images/position/position4.pdf
new file mode 100644
index 0000000..59cd05c
--- /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.pdf b/buch/papers/nav/images/position/position5.pdf
new file mode 100644
index 0000000..5960392
--- /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}
+