diff options
Diffstat (limited to '')
| -rw-r--r-- | vorlesungen/slides/7/images/Makefile | 12 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/rodriguez.jpg | bin | 0 -> 168776 bytes | |||
| -rw-r--r-- | vorlesungen/slides/7/images/rodriguez.png | bin | 0 -> 261798 bytes | |||
| -rw-r--r-- | vorlesungen/slides/7/images/rodriguez.pov | 118 | ||||
| -rw-r--r-- | vorlesungen/slides/7/parameter.tex | 17 |
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 Binary files differnew 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 Binary files differnew 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} |
