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-rw-r--r--vorlesungen/slides/7/images/Makefile12
-rw-r--r--vorlesungen/slides/7/images/rodriguez.jpgbin0 -> 168776 bytes
-rw-r--r--vorlesungen/slides/7/images/rodriguez.pngbin0 -> 261798 bytes
-rw-r--r--vorlesungen/slides/7/images/rodriguez.pov118
-rw-r--r--vorlesungen/slides/7/parameter.tex17
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
Binary files differ
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
Binary files differ
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}