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+\documentclass[12pt, a4paper]{article}
+
+%packages
+\usepackage[ngerman]{babel}
+\usepackage[utf8x]{inputenc}
+%Formel packages
+\usepackage{amsmath}
+\usepackage{amsthm}
+\usepackage{amsbsy}
+\usepackage{amssymb}
+
+
+\usepackage{enumerate}
+
+
+\begin{document}
+
+\section*{Computer Graphics - Excercise 2}
+\begin{align*}
+	f(u,v) = R \begin{pmatrix} cos(u) \\ sin(u) \\ 0 \end{pmatrix} + r \begin{pmatrix} cos(u) \times cos(v) \\ sin(u) \times cos(v) \\ sin(v) \end{pmatrix}
+\end{align*}
+\subsection*{2.1}
+\subsection*{a)}
+\begin{align*}
+		\frac {\delta f }{\delta u} (u,v) &= \begin{pmatrix}  R (-sin(u)) + r (cos(v) \times -sin(u)) \\ R \times cos(u) + r(cos(v)\times cos(u)) \\ 0 \end{pmatrix}\\
+		\\
+		\frac {\delta f }{\delta v} (u,v) &= \begin{pmatrix}   r (cos(u) \times (-sin(v))) \\ r(-sin(v) \times sin(u)) \\ r \times cos(v) \end{pmatrix}\\
+		\\
+		\Rightarrow Jacobian:\\
+		J_f (u,f) &=\begin{pmatrix} R \times (-sin(u)) +r (cos(v) \times -sin(u)) & r (cos(u) \times (-sin(v))) \\ sin(u) \times cos(v) & r(-sin(v) \times sin(u)) \\ 0 & r \times cos(v)\end{pmatrix}\\
+\end{align*}
+\subsection*{b)}
+$I_{\tau}^s = \begin{pmatrix} E & F \\ F & G \end{pmatrix}$ mit $s_u=\frac {\delta f }{\delta u} (u,v), s_v=\frac {\delta f }{\delta v} (u,v)\\
+\\
+E = ||s_u||^2 = (r(cos(u))+R)^2\\
+\\
+F = < s_u , s_v > = 0\\
+\\
+G = ||s_v||^2 = r^2\\$
+\\
+$\Rightarrow I_{\tau}^f = \begin{pmatrix} (r(cos(u))+R)^2 & 0 \\ 0 & r^2 \end{pmatrix}$
+
+\subsection*{c)}
+
+Aus der Vorlesung: $dA = \sqrt{det I_{\tau}^f} \,du\,dv$\\
+\begin{align*}
+\Rightarrow dA &= \sqrt{det \begin{pmatrix} (r(cos(u))+R)^2 & 0 \\ 0 & r^2 \end{pmatrix}} \,du\,dv\\
+\Rightarrow dA &=  r(r(cos(u))+R) \,du\,dv\\
+\end{align*}
+\\
+$\Rightarrow A = \int_{0}^{2\pi} \int_{0}^{2\pi}  r(r(cos(u))+R) \,du\,dv = 2 \pi r \times  \int_{0}^{2\pi}  r(cos(u))+R \,dv =\\\\ 2 \pi r [Rv + r(sin(v)]_{0}^{2\pi} = 2 \pi r \times (2\pi R) = \underline{\underline{4\pi^2Rr}} $
+t\end{document}
+