diff --git a/mr/ubB/mrB.pdf b/mr/ubB/mrB.pdf index 58c697f..8126324 100644 --- a/mr/ubB/mrB.pdf +++ b/mr/ubB/mrB.pdf Binary files differ diff --git a/mr/ubB/mrB.tex b/mr/ubB/mrB.tex index 5d77ae9..bed3353 100644 --- a/mr/ubB/mrB.tex +++ b/mr/ubB/mrB.tex @@ -107,11 +107,11 @@ \Aufgabe{Reeds-Shepp-Curves}{8} \begin{enumerate}[(a)] \item As the tangent is always perpendicular to the radius there are right triangles. So for $r_1=r_2=r$ we can calculate:\\ - $d=2\cdot \sqrt{dist(\mathbf{s'},\mathbf{g'})^2-r^2}$\\ + $d=2\cdot \sqrt{\left(\frac{1}{2}dist(\mathbf{s'},\mathbf{g'})\right)^2-r^2}$\\ For $r_1\not=r_2$ we can use:\\ $d=\sqrt{dist(\mathbf{s'},\mathbf{g'})^2-(r_1+r_2)^2}$\\ There geometrical explanation is to translate $r_2$ and append it to $r_1$. Then there is only one right triangle and we again can calculate the pythagorean. - \item $\delta(\alpha_r,\mathbf{s'},\mathbf{g'},\alpha_l)=r\alpha_r+d+r\alpha_l=r\alpha_r+2\cdot\sqrt{dist(\mathbf{s'},\mathbf{g'})^2-r^2}+r\alpha_l$ + \item $\delta(\alpha_r,\mathbf{s'},\mathbf{g'},\alpha_l)=r\alpha_r+d+r\alpha_l=r\alpha_r+2\cdot\sqrt{\left(\frac{1}{2}dist(\mathbf{s'},\mathbf{g'})\right)^2-r^2}+r\alpha_l$ \item $\delta(\alpha_r,\mathbf{s'},\mathbf{g'},\alpha_l)=r_1\alpha_r+d+r_2\alpha_l=r_1\alpha_r+\sqrt{dist(\mathbf{s'},\mathbf{g'})^2-(r_1+r_2)^2}+r_2\alpha_l$ \end{enumerate} \end{document}