18 files changed, 213 insertions, 30 deletions

diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile
index c9dcacc..bbdea2f 100644
--- a/buch/papers/nav/images/Makefile
+++ b/buch/papers/nav/images/Makefile
@@ -50,7 +50,8 @@ DREIECKE3D =								\
 	dreieck3d4.pdf							\
 	dreieck3d5.pdf							\
 	dreieck3d6.pdf							\
-	dreieck3d7.pdf
+	dreieck3d7.pdf							\
+	dreieck3d8.pdf
 
 dreiecke3d: $(DREIECKE3D)
 
@@ -106,3 +107,10 @@ dreieck3d7.jpg:	dreieck3d7.png
 dreieck3d7.pdf:	dreieck3d7.tex dreieck3d7.jpg
 	pdflatex dreieck3d7.tex
 
+dreieck3d8.png:	dreieck3d8.pov common.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
+
diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc
index 33d9384..e2a1ed0 100644
--- a/buch/papers/nav/images/common.inc
+++ b/buch/papers/nav/images/common.inc
@@ -97,13 +97,13 @@ union {
 	}
 #end
 
-#macro winkel(w, p, q, staerke)
+#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 { <0, 0, 0>, 1 + staerke }
-		cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), 0.4 }
+		cone { <0, 0, 0>, 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 }
 	}
@@ -113,8 +113,30 @@ union {
 	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
+
 #declare fett = 0.015;
-#declare fine = 0.010;
+#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>;
diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf
new file mode 100644
index 0000000..015bce7
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d1.pdf
diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov
index 8afe60e..e491075 100644
--- a/buch/papers/nav/images/dreieck3d1.pov
+++ b/buch/papers/nav/images/dreieck3d1.pov
@@ -12,9 +12,9 @@ union {
 	punkt(A, fett)
 	punkt(B, fett)
 	punkt(C, fett)
-	punkt(P, fine)
-	seite(B, P, fine)
-	seite(C, P, fine)
+	punkt(P, fein)
+	seite(B, P, fein)
+	seite(C, P, fein)
 	pigment {
 		color dreieckfarbe
 	}
@@ -25,7 +25,7 @@ union {
 }
 
 object {
-	winkel(A, B, C, fine)
+	winkel(A, B, C, fein, gross)
 	pigment {
 		color rot
 	}
@@ -36,7 +36,7 @@ object {
 }
 
 object {
-	winkel(B, C, A, fine)
+	winkel(B, C, A, fein, gross)
 	pigment {
 		color gruen
 	}
@@ -47,7 +47,7 @@ object {
 }
 
 object {
-	winkel(C, A, B, fine)
+	winkel(C, A, B, fein, gross)
 	pigment {
 		color blau
 	}
diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf
new file mode 100644
index 0000000..6b3f09d
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d2.pdf
diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov
index c23a54c..c0625ce 100644
--- a/buch/papers/nav/images/dreieck3d2.pov
+++ b/buch/papers/nav/images/dreieck3d2.pov
@@ -12,9 +12,9 @@ union {
 	punkt(A, fett)
 	punkt(B, fett)
 	punkt(C, fett)
-	punkt(P, fine)
-	seite(B, P, fine)
-	seite(C, P, fine)
+	punkt(P, fein)
+	seite(B, P, fein)
+	seite(C, P, fein)
 	pigment {
 		color dreieckfarbe
 	}
diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf
new file mode 100644
index 0000000..7d79455
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d3.pdf
diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov
index f2496b5..b6f64d5 100644
--- a/buch/papers/nav/images/dreieck3d3.pov
+++ b/buch/papers/nav/images/dreieck3d3.pov
@@ -12,9 +12,9 @@ union {
 	punkt(A, fett)
 	punkt(B, fett)
 	punkt(C, fett)
-	punkt(P, fine)
-	seite(B, P, fine)
-	seite(C, P, fine)
+	punkt(P, fein)
+	seite(B, P, fein)
+	seite(C, P, fein)
 	pigment {
 		color dreieckfarbe
 	}
@@ -25,7 +25,7 @@ union {
 }
 
 object {
-	winkel(A, B, C, fine)
+	winkel(A, B, C, fein, gross)
 	pigment {
 		color rot
 	}
diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf
new file mode 100644
index 0000000..e1ea757
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d4.pdf
diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov
index bddcf7c..b6f17e3 100644
--- a/buch/papers/nav/images/dreieck3d4.pov
+++ b/buch/papers/nav/images/dreieck3d4.pov
@@ -6,9 +6,9 @@
 #include "common.inc"
 
 union {
-	seite(A, B, fine)
-	seite(A, C, fine)
-	punkt(A, fine)
+	seite(A, B, fein)
+	seite(A, C, fein)
+	punkt(A, fein)
 	punkt(B, fett)
 	punkt(C, fett)
 	punkt(P, fett)
@@ -25,7 +25,7 @@ union {
 }
 
 object {
-	winkel(B, C, P, fine)
+	winkel(B, C, P, fein, gross)
 	pigment {
 		color rgb<0.6,0.4,0.2>
 	}
diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf
new file mode 100644
index 0000000..6848331
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d5.pdf
diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov
index 32fc9e6..188f181 100644
--- a/buch/papers/nav/images/dreieck3d5.pov
+++ b/buch/papers/nav/images/dreieck3d5.pov
@@ -6,9 +6,9 @@
 #include "common.inc"
 
 union {
-	seite(A, B, fine)
-	seite(A, C, fine)
-	punkt(A, fine)
+	seite(A, B, fein)
+	seite(A, C, fein)
+	punkt(A, fein)
 	punkt(B, fett)
 	punkt(C, fett)
 	punkt(P, fett)
diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov
index 7611950..191a1e7 100644
--- a/buch/papers/nav/images/dreieck3d6.pov
+++ b/buch/papers/nav/images/dreieck3d6.pov
@@ -25,7 +25,7 @@ union {
 }
 
 object {
-	winkel(B, A, P, fine)
+	winkel(B, A, P, fein, gross)
 	pigment {
 		color rgb<0.6,0.2,0.6>
 	}
diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov
index fa48f5b..aae5c6c 100644
--- a/buch/papers/nav/images/dreieck3d7.pov
+++ b/buch/papers/nav/images/dreieck3d7.pov
@@ -10,13 +10,13 @@ union {
 	seite(A, P, fett)
 	seite(C, P, fett)
 
-	seite(A, B, fine)
-	seite(B, C, fine)
-	seite(B, P, fine)
+	seite(A, B, fein)
+	seite(B, C, fein)
+	seite(B, P, fein)
 	punkt(A, fett)
 	punkt(C, fett)
 	punkt(P, fett)
-	punkt(B, fine)
+	punkt(B, fein)
 	pigment {
 		color dreieckfarbe
 	}
@@ -27,7 +27,7 @@ union {
 }
 
 object {
-	winkel(A, P, C, fine)
+	winkel(A, P, C, fein, gross)
 	pigment {
 		color rgb<0.4,0.4,1>
 	}
diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg
new file mode 100644
index 0000000..52bd25e
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.jpg
diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf
new file mode 100644
index 0000000..9d630aa
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.pdf
diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov
new file mode 100644
index 0000000..9e9921a
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.pov
@@ -0,0 +1,96 @@
+//
+// dreiecke3d8.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+union {
+	seite(A, B, fett)
+	seite(B, C, fett)
+	seite(A, C, fett)
+	seite(A, P, fein)
+	seite(B, P, fett)
+	seite(C, P, fett)
+	punkt(A, fett)
+	punkt(B, fett)
+	punkt(C, fett)
+	punkt(P, fett)
+	pigment {
+		color dreieckfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, B, C, fein, klein)
+	pigment {
+		color rot
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(B, C, A, fein, klein)
+	pigment {
+		color gruen
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(C, A, B, fein, gross)
+	pigment {
+		color blau
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(A, P, C, fein/2, gross)
+	pigment {
+		color rgb<0.8,0,0.8>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(B, P, C, fein, klein)
+	pigment {
+		color rgb<1,0.8,0>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+object {
+	winkel(B, P, A, fein/2, gross)
+	pigment {
+		color rgb<0.4,0.6,0.8>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+dreieck(A, B, C, White)
+
+
diff --git a/buch/papers/nav/images/dreieck3d8.tex b/buch/papers/nav/images/dreieck3d8.tex
new file mode 100644
index 0000000..c59c7b0
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.tex
@@ -0,0 +1,57 @@
+%
+% dreieck3d8.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}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{dreieck3d8.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];
+}{}
+
+\node at (0.7,3.8) {$A$};
+\node at (-3.4,-0.8) {$B$};
+\node at (3.3,-2.1) {$C$};
+\node at (-1.4,-3.5) {$P$};
+
+\node at (-1.9,2.1) {$c$};
+\node at (-0.2,-1.2) {$a$};
+\node at (2.6,1.5) {$b$};
+\node at (-0.8,0) {$l$};
+
+\node at (-2.6,-2.2) {$p_b$};
+\node at (1,-2.9) {$p_c$};
+
+\node at (0.7,3.3) {$\alpha$};
+\node at (0.8,2.85) {$\omega$};
+\node at (-2.6,-0.6) {$\beta$};
+\node at (2.3,-1.2) {$\gamma$};
+\node at (-2.6,-1.3) {$\beta_1$};
+\node at (-2.1,-0.8) {$\kappa$};
+
+\end{tikzpicture}
+
+\end{document}
+