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Fiete Winter
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add figure from appendix B.1
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‎B_derivations/fig01/README.md‎

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![Fig](fig1.png)
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![Fig](fig2.png)
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![Fig](fig3.png)
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minimum and maximum wavenumber vector for circular region -- case 1
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Bash:
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```Bash
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$ pdflatex fig1.tex
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```
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minimum and maximum wavenumber vector for circular region -- case 2
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Bash:
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```Bash
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$ pdflatex fig2.tex
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```
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minimum and maximum wavenumber vector for circular region -- case 3
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Bash:
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```Bash
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$ pdflatex fig3.tex
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```

‎B_derivations/fig01/fig1.pdf‎

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‎B_derivations/fig01/fig1.png‎

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‎B_derivations/fig01/fig1.tex‎

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% minimum and maximum wavenumber vector for circular region -- case 1
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%*****************************************************************************
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% Copyright (c) 2019 Fiete Winter *
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% Institut fuer Nachrichtentechnik *
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% Universitaet Rostock *
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% Richard-Wagner-Strasse 31, 18119 Rostock, Germany *
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% *
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% This file is part of the supplementary material for Fiete Winter's *
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% PhD thesis *
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% *
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% You can redistribute the material and/or modify it under the terms of the *
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% GNU General Public License as published by the Free Software Foundation *
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% , either version 3 of the License, or (at your option) any later version. *
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% *
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% This Material is distributed in the hope that it will be useful, but *
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% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY *
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% or FITNESS FOR A PARTICULAR PURPOSE. *
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% See the GNU General Public License for more details. *
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% *
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% You should have received a copy of the GNU General Public License along *
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% with this program. If not, see <http://www.gnu.org/licenses/>. *
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% *
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% http://github.com/fietew/phd-thesis fiete.winter@gmail.com *
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%*****************************************************************************
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\documentclass{standalone}
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\usepackage{import}
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\input{../../preamble/standalone}
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\begin{document}
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\begin{tikzpicture}
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\pgfmathsetmacro{\Rvec}{1.0}
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\pgfmathsetmacro{\Rdashed}{2.5}
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\pgfmathsetmacro{\Rls}{5.0}
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\pgfmathsetmacro{\Ru}{\Rls-0.1}
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\pgfmathsetmacro{\phider}{0}
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\pgfmathsetmacro{\Rder}{2.0}
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\pgfmathsetmacro{\phips}{-30}
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\pgfmathsetmacro{\Rps}{2}
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\pgfmathsetmacro{\rl}{0.7}
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\pgfmathsetmacro{\Rl}{0.85}
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\pgfmathsetmacro{\phil}{70}
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\pgfmathsetmacro{\phimin}{-180}
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\pgfmathsetmacro{\phimax}{+0}
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\coordinate (origin) at (0,0);
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\fill[fill=black!30] (\phil:\rl) circle (\Rl);
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\coordinate (center) at (\phil:\rl);
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\node[circle, fill=black, inner sep=1pt, label={90:$\sfpos[subscript=h]$}]
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at (center) {};
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\draw(center) -- +(180:\Rl) node[midway,above=-3pt,sloped]{\footnotesize
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$\sfR[subscript=h]$};
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\node[above right=0.25cm of center]{$\sfcircle[subscript=h]$};
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%%\coordinate (xmin) at (\phimin:\Rmax);
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%%\coordinate (xmax) at (\phimax:\Rmax);
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%
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\coordinate (kmax) at (\phimax:\Rvec);
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\coordinate (kmin) at (\phimin:\Rvec);
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%\draw(center) -- (xmax) node[midway,above=-3pt,sloped]{\footnotesize $R_l$};
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%\draw(center) -- (xmin);
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%\dotMarkRightAngle[size=4pt](center,xmax,origin);
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%\dotMarkRightAngle[size=4pt](origin,xmin,center);
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\draw[draw=black] ($(-70:\Rls)+(0,\Rls)$) arc (-70:-110:\Rls);
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\draw[draw=black,-latex'] ($(-75:\Ru)+(0,\Rls)$) arc (-75:-70:\Ru)
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node[above, sloped, midway] {$u$};
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\foreach \phils in {-105, -100, -95, -85, -80, -75}
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{
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\node[loudspeaker,
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fill=activecolor,
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transform shape,
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rotate=\phils-180,
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anchor=cone] at ($(\phils:\Rls)+(0,\Rls)$) {};
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}
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\node[loudspeaker,
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fill=activecolor,
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transform shape,
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rotate=90,
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anchor=cone,
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label={180:$\sfpossec$}] (ls) {};
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\coordinate[label={-90:$\sftangentsec$}] (derivative) at (\phider:\Rder);
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\draw[-latex'] (0,0) -- (derivative);
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\coordinate[label={90:$\sfnormalsec$}] (nls) at (0,\Rder);
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\draw[-latex'] (0,0) -- (nls);
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\coordinate (kmaxu) at ($(derivative)!(kmax)!(0,0)$);
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\draw[draw=red, thick] (kmaxu) -- (0,0)
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node[below=0.75cm, pos=0.25,anchor=south]
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{\color{red}$\sfknorm^{\max}_{\sfgreens,\sftangentsec}$};
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\draw[dashed] (kmaxu) -- (kmax);
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\coordinate (kminu) at ($(derivative)!(kmin)!(0,0)$);
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\draw[draw=blue, thick] (kminu) -- (0,0)
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node[below=0.75cm, pos=0.35, anchor=south]
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{\color{blue}$\sfknorm^{\min}_{\sfgreens,\sftangentsec}$};
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\draw[dashed] (kminu) -- (kmin);
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\draw[red, thick] (0,0) -- (kmax);
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\draw[blue, thick] (0,0) -- (kmin);
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%
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\end{tikzpicture}
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%
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\end{document}

‎B_derivations/fig01/fig2.pdf‎

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‎B_derivations/fig01/fig2.png‎

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‎B_derivations/fig01/fig2.tex‎

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% minimum and maximum wavenumber vector for circular region -- case 2
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%*****************************************************************************
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% Copyright (c) 2019 Fiete Winter *
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% Institut fuer Nachrichtentechnik *
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% Universitaet Rostock *
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% Richard-Wagner-Strasse 31, 18119 Rostock, Germany *
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% *
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% This file is part of the supplementary material for Fiete Winter's *
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% PhD thesis *
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% *
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% You can redistribute the material and/or modify it under the terms of the *
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% GNU General Public License as published by the Free Software Foundation *
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% , either version 3 of the License, or (at your option) any later version. *
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% *
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% This Material is distributed in the hope that it will be useful, but *
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% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY *
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% or FITNESS FOR A PARTICULAR PURPOSE. *
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% See the GNU General Public License for more details. *
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% *
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% You should have received a copy of the GNU General Public License along *
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% with this program. If not, see <http://www.gnu.org/licenses/>. *
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% *
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% http://github.com/fietew/phd-thesis fiete.winter@gmail.com *
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%*****************************************************************************
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\documentclass{standalone}
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\usepackage{import}
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\input{../../preamble/standalone}
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\begin{document}
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\begin{tikzpicture}
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\pgfmathsetmacro{\Rvec}{1.0}
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\pgfmathsetmacro{\Rdashed}{2.5}
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\pgfmathsetmacro{\Rls}{5.0}
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\pgfmathsetmacro{\Ru}{\Rls-0.1}
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\pgfmathsetmacro{\phider}{0}
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\pgfmathsetmacro{\Rder}{2.0}
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\pgfmathsetmacro{\phips}{-30}
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\pgfmathsetmacro{\Rps}{2}
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\pgfmathsetmacro{\rl}{1.4}
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\pgfmathsetmacro{\Rl}{0.85}
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\pgfmathsetmacro{\phil}{30}
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\pgfmathsetmacro{\Rmax}{sqrt(\rl*\rl - \Rl*\Rl)}
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\pgfmathsetmacro{\phimin}{\phil+asin(\Rl/\rl)}
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\pgfmathsetmacro{\phimax}{0}
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\coordinate (origin) at (0,0);
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\fill[fill=black!30] (\phil:\rl) circle (\Rl);
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\coordinate (center) at (\phil:\rl);
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\node[circle, fill=black, inner sep=1pt, label={90:$\sfpos[subscript=h]$}]
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at (center) {};
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\node[above right=0.25cm of center]{$\sfcircle[subscript=h]$};
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\draw[dashed] (0,0) -- (\phimin:\Rdashed);
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\coordinate (xmin) at (\phimin:\Rmax);
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\coordinate (xmax) at (\phimax:\Rmax);
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\coordinate (kmax) at (\phimax:\Rvec);
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\coordinate (kmin) at (\phimin:\Rvec);
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\draw(center) -- (xmin) node[midway,below=-3pt,sloped]{\footnotesize $
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\sfR[subscript=h]$};
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\dotMarkRightAngle[size=4pt](origin,xmin,center);
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\draw[draw=black] ($(-70:\Rls)+(0,\Rls)$) arc (-70:-110:\Rls);
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\draw[draw=black,-latex'] ($(-75:\Ru)+(0,\Rls)$) arc (-75:-70:\Ru)
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node[above, sloped, midway] {$u$};
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\foreach \phils in {-105, -100, -95, -85, -80, -75}
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{
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\node[loudspeaker,
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fill=activecolor,
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transform shape,
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rotate=\phils-180,
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anchor=cone] at ($(\phils:\Rls)+(0,\Rls)$) {};
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}
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\node[loudspeaker,
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fill=activecolor,
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transform shape,
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rotate=90,
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anchor=cone,
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label={180:$\sfpossec$}] (ls) {};
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\coordinate[label={-90:$\sftangentsec$}] (derivative) at (\phider:\Rder);
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\draw[-latex'] (0,0) -- (derivative);
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\coordinate[label={90:$\sfnormalsec$}] (nls) at (0,\Rder);
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\draw[-latex'] (0,0) -- (nls);
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\coordinate (kmaxu) at ($(derivative)!(kmax)!(0,0)$);
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\draw[draw=red, thick] (kmaxu) -- (0,0)
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node[below=0.75cm, pos=0.25,anchor=south]
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{\color{red}$\sfknorm^{\max}_{\sfgreens,\sftangentsec}$};
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\draw[dashed] (kmaxu) -- (kmax);
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\coordinate (kminu) at ($(derivative)!(kmin)!(0,0)$);
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\coordinate (kmint) at ($(nls)!(kmin)!(0,0)$);
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%\draw[red, thick] (0,0) -- (kmax);
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%
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\draw[draw=blue, thick] (kmint) -- (kmin) node[above=0.75cm,
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pos=0,anchor=north] {\color{blue}$\sfknorm^{\min}_{\sfgreens,\sftangentsec}$};
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\draw[dashed] (kminu) -- (kmin);
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\draw[-latex',blue, thick] (origin) -- (kmin);
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%
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\end{tikzpicture}
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%
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\end{document}

‎B_derivations/fig01/fig3.pdf‎

35.4 KB
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‎B_derivations/fig01/fig3.png‎

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