theorie 1 latex added
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exercise1/Theorie.aux
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This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2018.9.7) 6 NOV 2018 16:07
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\documentclass[12pt, a4paper]{scrbook}
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%packages
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\usepackage[ngerman]{babel}
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\usepackage[utf8x]{inputenc}
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%Formel packages
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\usepackage{amsmath}
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\usepackage{amsthm}
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\usepackage{amsbsy}
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\usepackage{amssymb}
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\usepackage{enumerate}
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\begin{document}
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\section*{Computer Graphics - Excercise 1}
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\subsection*{1.1.1}
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\subsection*{a)}
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\begin{itemize}
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\item Matrix Multiplication $\equiv$ transformation
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\item Inverse of a transformation $\tilde{T}^{-1}$ \\
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\begin{align*}
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\Rightarrow && \tilde{T}*\tilde{T}^{-1} &= \tilde{T}^{-1}*\tilde{T} = \tilde{E} && \left |\ *\tilde{p} \right. \\
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&&\tilde{T}^{-1}*\tilde{T}*\tilde{p} &= \tilde{E}*\tilde{p} && \left |\ \tilde{T}*\tilde{p}=\tilde{p'} \right. \\
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\Rightarrow && \tilde{E}*\tilde{p} = \tilde{p}&, \hspace{1em} \tilde{T}^{-1}*\tilde{p'} = \tilde{p} \\
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\end{align*}
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\end{itemize}
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\subsection*{b)}
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\subsection*{1.1.2}
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\subsection*{a)}
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\begin{gather*}
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\begin{pmatrix} 1 & 0 & 0 \\ 0&1&0\\ 0&0&1 \\ \end{pmatrix} * \begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} =\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ z_1&z_2&\cdots&z_n\\ y_1&y_2&\cdots&y_n \\ \end{pmatrix}
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\end{gather*}
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\subsection*{b)}
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\begin{gather*}
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\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} * \begin{pmatrix} 1 \\ 1 \\ \vdots \\ 1 \\ \end{pmatrix} =
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\begin{pmatrix} \sum\limits_{i=1} x \\ \sum\limits_{i=1} y \\ \sum\limits_{i=1} z \end{pmatrix}
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\end{gather*}
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\subsection*{c)}
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\begin{align*}
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L(p) &= length(p_x - ((p_x \cdot (\vec{e} + \vec{d} * t)) *\vec{d} * t) - \vec{e}) \\
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Vector &= ( L(p_x), L(p_{x+1}), ... , L(p_{x+n})) \hspace{6em} n \equiv Anz. Punkte \\
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\end{align*}
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Berechnung:
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\end{document}
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Reference in a new issue