From a90d54e578b7d309ba680d5fd5f6c8721b082096 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 6 May 2021 17:57:06 +0200
Subject: new slide

---
 vorlesungen/slides/7/interpolation.tex | 105 +++++++++++++++++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 vorlesungen/slides/7/interpolation.tex

(limited to 'vorlesungen/slides/7/interpolation.tex')

diff --git a/vorlesungen/slides/7/interpolation.tex b/vorlesungen/slides/7/interpolation.tex
new file mode 100644
index 0000000..3d40d7b
--- /dev/null
+++ b/vorlesungen/slides/7/interpolation.tex
@@ -0,0 +1,105 @@
+%
+% 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)}
+\end{align*}
+\end{block}}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<10->{%
+\begin{block}{Animation}
+\centering
+\bild{11}{i00}
+\bild{12}{i01}
+\bild{13}{i02}
+\bild{14}{i03}
+\bild{15}{i04}
+\bild{16}{i05}
+\bild{17}{i06}
+\bild{18}{i07}
+\bild{19}{i08}
+\bild{20}{i09}
+\bild{21}{i10}
+\bild{22}{i11}
+\bild{23}{i12}
+\bild{24}{i13}
+\bild{25}{i14}
+\bild{26}{i15}
+\bild{27}{i16}
+\bild{28}{i17}
+\bild{29}{i18}
+\bild{30}{i19}
+\bild{31}{i20}
+\bild{32}{i21}
+\bild{33}{i22}
+\bild{34}{i23}
+\bild{35}{i24}
+\bild{36}{i25}
+\bild{37}{i26}
+\bild{38}{i27}
+\bild{39}{i28}
+\bild{40}{i29}
+\bild{41}{i30}
+\bild{42}{i31}
+\bild{43}{i32}
+\bild{44}{i33}
+\bild{45}{i34}
+\bild{46}{i35}
+\bild{47}{i36}
+\bild{48}{i37}
+\bild{49}{i38}
+\bild{50}{i39}
+\bild{51}{i40}
+\bild{52}{i41}
+\bild{53}{i42}
+\bild{54}{i43}
+\bild{55}{i44}
+\bild{56}{i45}
+\bild{57}{i46}
+\bild{58}{i47}
+\bild{59}{i48}
+\bild{60}{i49}
+\bild{61}{i50}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1

