add rodriguez image

5 files changed, 144 insertions, 3 deletions

diff --git a/vorlesungen/slides/7/images/Makefile b/vorlesungen/slides/7/images/Makefile
new file mode 100644
index 0000000..1b9590d
--- /dev/null
+++ b/vorlesungen/slides/7/images/Makefile
@@ -0,0 +1,12 @@
+#
+# Makefile -- Illustrationen zu 
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+# 
+all:	rodriguez.jpg
+
+rodriguez.png:	rodriguez.pov
+	povray +A0.1 -W1920 -H1080 -Orodriguez.png rodriguez.pov
+
+rodriguez.jpg:	rodriguez.png 
+	convert -extract 1740x1070+135+10 rodriguez.png rodriguez.jpg
diff --git a/vorlesungen/slides/7/images/rodriguez.jpg b/vorlesungen/slides/7/images/rodriguez.jpg
new file mode 100644
index 0000000..5c49700
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.jpg
diff --git a/vorlesungen/slides/7/images/rodriguez.png b/vorlesungen/slides/7/images/rodriguez.png
new file mode 100644
index 0000000..6d9e9e4
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.png
diff --git a/vorlesungen/slides/7/images/rodriguez.pov b/vorlesungen/slides/7/images/rodriguez.pov
new file mode 100644
index 0000000..07aec19
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.pov
@@ -0,0 +1,118 @@
+//
+// rodriguez.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.020;
+#declare O = <0, 0, 0>;
+#declare at = 0.015;
+
+camera {
+	location <8, 15, -50>
+	look_at <0.1, 0.475, 0>
+	right 16/9 * x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<-4, 20, -50> color White
+	area_light <1,0,0> <0,0,1>, 10, 10
+	adaptive 1
+	jitter
+}
+
+sky_sphere {
+	pigment {
+		color rgb<1,1,1>
+	}
+}
+
+#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 K = vnormalize(<0.2,1,0.1>);
+#declare X = vnormalize(<1.1,1,-1.2>);
+#declare O = <0,0,0>;
+
+#declare r = vlength(vcross(K, X)) / vlength(K);
+
+#declare l = 1.0;
+
+arrow(< -l,  0,  0 >, < l, 0, 0 >, at, White)
+arrow(<  0,  0, -l >, < 0, 0, l >, at, White)
+arrow(<  0, -l,  0 >, < 0, l, 0 >, at, White)
+
+arrow(O, X, at, Red)
+arrow(O, K, at, Blue)
+
+#macro punkt(H,phi)
+	((H-vdot(K,H)*K)*cos(phi) + vcross(K,H)*sin(phi) + vdot(K,X)*K)
+#end
+
+cone { vdot(K, X) * K, r, O, 0
+	pigment {
+		color rgbt<0.6,0.6,0.6,0.5>
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+
+union {
+	#declare phistep = pi / 100;
+	#declare phi = 0;
+	#while (phi < 2 * pi - phistep/2) 
+		sphere { punkt(K, phi), at/2 }
+		cylinder {
+			punkt(X, phi),
+			punkt(X, phi + phistep),
+			at/2
+		}
+		#declare phi = phi + phistep;
+	#end
+	pigment {
+		color Orange
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+arrow(vdot(K,X)*K, punkt(X, 0), at, Yellow)
+#declare Darkgreen = rgb<0,0.5,0>;
+arrow(vdot(K,X)*K, punkt(X, pi/2), at, Darkgreen)
diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index ec129bb..b719207 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -4,6 +4,7 @@
 % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 %
 \bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
 \begin{frame}[t]
 \setlength{\abovedisplayskip}{5pt}
 \setlength{\belowdisplayskip}{5pt}
@@ -41,17 +42,27 @@ $\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
 \[
 \vec{x}
 \mapsto
+(\vec{x} -(\vec{k}\cdot\vec{x})\vec{k})
 \cos\omega
-\vec{x}
 +
 (\vec{k}\times\vec{x})\sin\omega
 +
-\vec{k}(\vec{k}\cdot\vec{x}) (1-\cos\omega)
+\vec{k}(\vec{k}\cdot\vec{x}) 
 \]
-XXX TODO: Bild für Rodriguez Formel
+\vspace{-40pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\node at (0,0) {\includegraphics[width=\textwidth]{../slides/7/images/rodriguez.jpg}};
+\node[color=red] at (1.6,-0.9) {$\vec{x}$};
+\node[color=blue] at (0.5,2) {$\vec{k}$};
+\node[color=darkgreen] at (-3,1.1) {$\vec{k}\times\vec{x}$};
+\node[color=yellow] at (2.2,-0.2) {$\vec{x}-(\vec{x}\cdot\vec{k})\vec{k}$};
+\end{tikzpicture}
+\end{center}
 \end{block}
 \end{column}
 \end{columns}
+\vspace{-15pt}
 {\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
 dreidimensionale Gruppe
 \end{frame}