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author | User-PC\User <thomas.reichlin@ost.ch> | 2021-05-07 11:27:42 +0200 |
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committer | User-PC\User <thomas.reichlin@ost.ch> | 2021-05-07 11:27:42 +0200 |
commit | 156548662016ee324ea78bc2a9d8b049730eb709 (patch) | |
tree | b859e5461c6224257ef0f22eec52cd47bf0f4ea7 /vorlesungen/slides/7/interpolation.tex | |
parent | Push (diff) | |
parent | new slide (diff) | |
download | SeminarMatrizen-156548662016ee324ea78bc2a9d8b049730eb709.tar.gz SeminarMatrizen-156548662016ee324ea78bc2a9d8b049730eb709.zip |
Merge remote-tracking branch 'Upload/master'
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-rw-r--r-- | vorlesungen/slides/7/interpolation.tex | 112 |
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diff --git a/vorlesungen/slides/7/interpolation.tex b/vorlesungen/slides/7/interpolation.tex new file mode 100644 index 0000000..249ee26 --- /dev/null +++ b/vorlesungen/slides/7/interpolation.tex @@ -0,0 +1,112 @@ +% +% interpolation.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\def\bild#1#2{\only<#1|handout:0>{\includegraphics[width=\textwidth]{../slides/7/images/interpolation/#2.png}}} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Interpolation} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Aufgabe} +Finde einen Weg $g(t)\in \operatorname{SO}(3)$ zwischen +$g_0\in\operatorname{SO}(3)$ +und +$g_1\in\operatorname{SO}(3)$: +\[ +g_0=g(0) +\quad\wedge\quad +g_1=g(1) +\] +\end{block} +\vspace{-10pt} +\uncover<2->{% +\begin{block}{Lösung} +$g_i=\exp(A_i) \uncover<3->{\Rightarrow A_i^t=-A_i}$ +\begin{align*} +\uncover<4->{A(t) &= (1-t)A_0 + tA_1}\uncover<8->{ \in \operatorname{so}(3)} +\\ +\uncover<5->{A(t)^t +&=(1-t)A_0^t + tA_1^t} +\\ +&\uncover<6->{= +-(1-t)A_0 - t A_1} +\uncover<7->{= +-A(t)} +\\ +\uncover<9->{\Rightarrow +g(t) &= \exp A(t) \in \operatorname{SO}(3)} +\\ +&\uncover<10->{\ne +\exp (\log(g_1g_0^{-1})t) g_0} +\end{align*} +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<11->{% +\begin{block}{Animation} +\centering +\ifthenelse{\boolean{presentation}}{ +\bild{12}{i00} +\bild{13}{i01} +\bild{14}{i02} +\bild{15}{i03} +\bild{16}{i04} +\bild{17}{i05} +\bild{18}{i06} +\bild{19}{i07} +\bild{20}{i08} +\bild{21}{i09} +\bild{22}{i10} +\bild{23}{i11} +\bild{24}{i12} +\bild{25}{i13} +\bild{26}{i14} +\bild{27}{i15} +\bild{28}{i16} +\bild{29}{i17} +\bild{30}{i18} +\bild{31}{i19} +\bild{32}{i20} +\bild{33}{i21} +\bild{34}{i22} +\bild{35}{i23} +\bild{36}{i24} +\bild{37}{i25} +\bild{38}{i26} +\bild{39}{i27} +\bild{40}{i28} +\bild{41}{i29} +\bild{42}{i30} +\bild{43}{i31} +\bild{44}{i32} +\bild{45}{i33} +\bild{46}{i34} +\bild{47}{i35} +\bild{48}{i36} +\bild{49}{i37} +\bild{50}{i38} +\bild{51}{i39} +\bild{52}{i40} +\bild{53}{i41} +\bild{54}{i42} +\bild{55}{i43} +\bild{56}{i44} +\bild{57}{i45} +\bild{58}{i46} +\bild{59}{i47} +\bild{60}{i48} +\bild{61}{i49} +\bild{62}{i50} +}{ +\includegraphics[width=\textwidth]{../slides/7/images/interpolation/i25.png} +} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |