diff options
author | Nao Pross <np@0hm.ch> | 2021-04-13 19:48:07 +0200 |
---|---|---|
committer | Nao Pross <np@0hm.ch> | 2021-04-13 19:48:07 +0200 |
commit | d1b602b59a428bea7a59655cd5af34a919e7acf5 (patch) | |
tree | c9ad2469eb5c287d60179e4b57f78373e977a4dc /vorlesungen/slides/7/drehanim.tex | |
parent | Add outline (diff) | |
parent | typos (diff) | |
download | SeminarMatrizen-d1b602b59a428bea7a59655cd5af34a919e7acf5.tar.gz SeminarMatrizen-d1b602b59a428bea7a59655cd5af34a919e7acf5.zip |
Merge branch 'master' of https://github.com/AndreasFMueller/SeminarMatrizen
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/7/drehanim.tex | 155 |
1 files changed, 155 insertions, 0 deletions
diff --git a/vorlesungen/slides/7/drehanim.tex b/vorlesungen/slides/7/drehanim.tex new file mode 100644 index 0000000..ac136f1 --- /dev/null +++ b/vorlesungen/slides/7/drehanim.tex @@ -0,0 +1,155 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup + +\definecolor{darkgreen}{rgb}{0,0.6,0} +\def\punkt#1#2{ ({\A*(#1)+\B*(#2)},{\C*(#1)+\D*(#2)}) } + +\makeatletter +\hoffset=-2cm +\advance\textwidth2cm +\hsize\textwidth +\columnwidth\textwidth +\makeatother + +\begin{frame}[t,plain] +\vspace{-5pt} +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\fill[color=white] (-4,-4) rectangle (9,4.5); + +\def\a{60} + +\pgfmathparse{tan(\a)} +\xdef\T{\pgfmathresult} + +\pgfmathparse{-sin(\a)*cos(\a)} +\xdef\S{\pgfmathresult} + +\pgfmathparse{1/cos(\a)} +\xdef\E{\pgfmathresult} + +\def\N{20} +\pgfmathparse{2*\N} +\xdef\Nzwei{\pgfmathresult} +\pgfmathparse{3*\N} +\xdef\Ndrei{\pgfmathresult} + +\node at (4.2,4.2) [below right] {\begin{minipage}{7cm} +\begin{block}{$\operatorname{SO}(2)\subset\operatorname{SL}_2(\mathbb{R})$} +\begin{itemize} +\item Thus most $A\in\operatorname{SL}_2(\mathbb{R})$ can be parametrized +as shear mappings and axis rescalings +\[ +A= +\begin{pmatrix}d&0\\0&d^{-1}\end{pmatrix} +\begin{pmatrix}1&s\\0&1\end{pmatrix} +\begin{pmatrix}1&0\\t&1\end{pmatrix} +\] +\item Most rotations can be decomposed into a product of +shear mappings and axis rescalings +\end{itemize} +\end{block} +\end{minipage}}; + +\foreach \d in {1,2,...,\Ndrei}{ + % Scherung in Y-Richtung + \ifnum \d>\N + \pgfmathparse{\T} + \else + \pgfmathparse{\T*(\d-1)/(\N-1)} + \fi + \xdef\t{\pgfmathresult} + + % Scherung in X-Richtung + \ifnum \d>\Nzwei + \xdef\s{\S} + \else + \ifnum \d<\N + \xdef\s{0} + \else + \ifnum \d=\N + \xdef\s{0} + \else + \pgfmathparse{\S*(\d-\N-1)/(\N-1)} + \xdef\s{\pgfmathresult} + \fi + \fi + \fi + + % Reskalierung der Achsen + \ifnum \d>\Nzwei + \pgfmathparse{exp(ln(\E)*(\d-2*\N-1)/(\N-1))} + \else + \pgfmathparse{1} + \fi + \xdef\e{\pgfmathresult} + + % Matrixelemente + \pgfmathparse{(\e)*((\s)*(\t)+1)} + \xdef\A{\pgfmathresult} + + \pgfmathparse{(\e)*(\s)} + \xdef\B{\pgfmathresult} + + \pgfmathparse{(\t)/(\e)} + \xdef\C{\pgfmathresult} + + \pgfmathparse{1/(\e)} + \xdef\D{\pgfmathresult} + + \only<\d>{ + \node at (5.0,-0.9) [below right] {$ + \begin{aligned} + t &= \t \\ + s &= \s \\ + d &= \e \\ + D &= \begin{pmatrix} + \A&\B\\ + \C&\D + \end{pmatrix} + \qquad + \only<60>{\checkmark} + \end{aligned} + $}; + } + + \begin{scope} + \clip (-4.05,-4.05) rectangle (4.05,4.05); + \only<\d>{ + \foreach \x in {-6,...,6}{ + \draw[color=blue,line width=0.5pt] + \punkt{\x}{-12} -- \punkt{\x}{12}; + } + \foreach \y in {-12,...,12}{ + \draw[color=darkgreen,line width=0.5pt] + \punkt{-6}{\y} -- \punkt{6}{\y}; + } + + \foreach \r in {1,2,3,4}{ + \draw[color=red] plot[domain=0:359,samples=360] + ({\r*(\A*cos(\x)+\B*sin(\x))},{\r*(\C*cos(\x)+\D*sin(\x))}) + -- + cycle; + } + } + \end{scope} + +% \uncover<\d>{ +% \node at (5,4) {\d}; +% } +} + +\draw[->] (-4,0) -- (4.2,0) coordinate[label={$x$}]; +\draw[->] (0,-4) -- (0,4.2) coordinate[label={right:$y$}]; + +\end{tikzpicture} +\end{center} +\end{frame} +\egroup |