Wie kann ich die implizite Funktion
\pgfmathsetmacro\xA{0}\pgfmathsetmacro\yA{0}\pgfmathsetmacro\xB{1}\pgfmathsetmacro\yB{0}\pgfmathsetmacro\xC{0.5}\pgfmathsetmacro\yC{0.5*sqrt(3)} f(x,y)=4*((x -\xA)^2 + (y - \yA)^2)*((x -\xB)^2 + (y -\yB)^2) -( ((x -\xC)^2 + (y -\yC)^2) -((x -\xA)^2 + (y -\yA)^2) -((x -\xB)^2 + (y -\yB)^2) )^2;
zusammen mit dem (hier) gleichseitigen Dreieck
\addplot[no marks] coordinates {(\xA,\yA) (\xB,\yB) (\xC,\yC) (\xA,\yA) };
am besten plotten?
Im Fall hier müsste sowas wie ein Kreisbogen unter der Seite AB rauskommen.
Meine Versuche sind nicht so prima; ich kenne mich mit gnuplot (sofern hier übh. nötig?) nicht so aus.
3 MWEs (gnuplot muss im Pfad sein):
% arara: pdflatex: {shell: yes}\documentclass[margin=5mm, tikz]{standalone}\usepackage{pgfplots}\pgfplotsset{compat=newest}\begin{document}% Ecken\pgfmathsetmacro\xA{0}\pgfmathsetmacro\yA{0}\pgfmathsetmacro\xB{1}\pgfmathsetmacro\yB{0}\pgfmathsetmacro\xC{0.5}\pgfmathsetmacro\yC{0.5*sqrt(3)}% A(0,0); B(1,0); C(0.5, 0.5*sqrt(3))\begin{tikzpicture}\begin{axis}[axis equal, title={$|AX| + |BX| = |CX|$}, ] \addplot +[%smooth, no markers, raw gnuplot, thick, %empty line = jump % not strictly necessary, ] gnuplot { f(x,y)=4*((x -\xA)^2 + (y - \yA)^2)*((x -\xB)^2 + (y -\yB)^2) -( ((x -\xC)^2 + (y -\yC)^2) -((x -\xA)^2 + (y -\yA)^2) -((x -\xB)^2 + (y -\yB)^2) )^2; set cntrparam levels discrete 0,0; set isosample 100,100; set size square; set view equal xy; set cont base; unset surface; splot f(x,y); }; \addlegendentry{$X$}\addplot[no marks] coordinates {(\xA,\yA) (\xB,\yB) (\xC,\yC) (\xA,\yA) }; \draw[fill=white] (\xA,\yA) circle (1.75pt) node[anchor=north east]{$A(\xA,\yA)$}; \draw[fill=white] (\xB,\yB) circle (1.75pt) node[anchor=north]{$B(\xB,\yB)$}; \draw[fill=white] (\xC,\yC) circle (1.75pt) node[anchor=east]{$C(\xC,\yC)$}; \end{axis}\end{tikzpicture}\begin{tikzpicture}\begin{axis}[ view = {0}{90}, axis equal, % restrict x to domain = -2.2:3 ] \addplot3 [contour gnuplot = {labels = false}, samples=10] { 2*sqrt((x -\xA)^2 + (y - \yA)^2)*sqrt((x -\xB)^2 + (y -\yB)^2) -( ((x -\xC)^2 + (y -\yC)^2) -((x -\xA)^2 + (y -\yA)^2) -((x -\xB)^2 + (y -\yB)^2) )^1 }; \addlegendentry{$X$}\addplot[no marks] coordinates {(\xA,\yA) (\xB,\yB) (\xC,\yC) (\xA,\yA) }; \draw[fill=white] (\xA,\yA) circle (1.75pt) node[anchor=north east]{$A(\xA,\yA)$}; \draw[fill=white] (\xB,\yB) circle (1.75pt) node[anchor=north]{$B(\xB,\yB)$}; \draw[fill=white] (\xC,\yC) circle (1.75pt) node[anchor=east]{$C(\xC,\yC)$}; \end{axis}\end{tikzpicture}\begin{tikzpicture}\begin{axis}[ axis equal, % restrict y to domain = -4:4, ] \addplot + [ no markers, raw gnuplot, thick, ] gnuplot { f(x,y)=4*((x -\xA)^2 + (y - \yA)^2)*((x -\xB)^2 + (y -\yB)^2) -( ((x -\xC)^2 + (y -\yC)^2) -((x -\xA)^2 + (y -\yA)^2) -((x -\xB)^2 + (y -\yB)^2) )^2; set contour base; set cntrparam levels discrete 0.01; unset surface; set view map; set isosamples 300; splot f(x,y); }; \addlegendentry{$X$}\addplot[no marks] coordinates {(\xA,\yA) (\xB,\yB) (\xC,\yC) (\xA,\yA) }; \draw[fill=white] (\xA,\yA) circle (1.75pt) node[anchor=north east]{$A(\xA,\yA)$}; \draw[fill=white] (\xB,\yB) circle (1.75pt) node[anchor=north]{$B(\xB,\yB)$}; \draw[fill=white] (\xC,\yC) circle (1.75pt) node[anchor=east]{$C(\xC,\yC)$}; \end{axis}\end{tikzpicture}\end{document}
