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exc 1 theorie

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fruitstaa 2018-11-12 11:17:10 +01:00
parent 3990b8984e
commit 6d484abbe3
2 changed files with 3 additions and 4 deletions
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exercise1/Theorie.pdf
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exercise1/Theorie.tex
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@ -120,7 +120,6 @@ $\Rightarrow S \times T \neq T \times S \Rightarrow$ does not commute\\
\begin{pmatrix} \sum\limits_{i=1} x_i \\ \sum\limits_{i=1} y_i \\ \sum\limits_{i=1} z_i \end{pmatrix} \begin{pmatrix} \sum\limits_{i=1} x_i \\ \sum\limits_{i=1} y_i \\ \sum\limits_{i=1} z_i \end{pmatrix}
\end{gather*} \end{gather*}
\subsection*{c)} \subsection*{c)}
\begin{align*} \begin{align*}
L(p) &= length(p_x - ((p_x \cdot (\vec{e} + \vec{d} \cdot t)) \cdot \vec{d} \cdot t) - \vec{e}) \\ L(p) &= length(p_x - ((p_x \cdot (\vec{e} + \vec{d} \cdot t)) \cdot \vec{d} \cdot t) - \vec{e}) \\
Vector &= ( L(p_x), L(p_{x+1}), ... , L(p_{x+n})) \hspace{6em} n \widehat{=} Anz. Punkte \\ Vector &= ( L(p_x), L(p_{x+1}), ... , L(p_{x+n})) \hspace{6em} n \widehat{=} Anz. Punkte \\
@ -144,9 +143,9 @@ e = \begin{pmatrix} 5 \\ 10 \\ 5 \\\end{pmatrix}= t;
p = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix} p = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix}
\end{gather*} \end{gather*}
\begin{gather*} \begin{gather*}
z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0 \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\ z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0 \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\
y_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(y_\phi) & -sin(y_\phi) & 0 \\ sin(y_\phi)&cos(y_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_y\\ y_\phi = \frac {\begin{pmatrix} 0\\1\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(y_\phi) & 0 & sin(y_\phi) \\ 0 &1 &0\\ -sin(z_\phi)&0&cos(y_\phi) \\ \end{pmatrix}=R_y\\
x_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(x_\phi) & -sin(x_\phi) & 0 \\ sin(x_\phi)&cos(x_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_x\\ x_\phi = \frac {\begin{pmatrix} 1\\0\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} 0 & 0 & 0 \\ 0 &cos(x_\phi)&-sin(x_\phi)\\ 0&sin(x_\phi)&cos(x_\phi) \\ \end{pmatrix}=R_x\\
M = R_x \times R_y \times R_z \\ M = R_x \times R_y \times R_z \\
\Rightarrow Vector = \begin{pmatrix} \Rightarrow Vector = \begin{pmatrix}
6.323746006808568\\ 6.323746006808568\\