Melhorando batatas TikZ

Question

Com as bibliotecas mathe calc, é possível fazer isso de forma um pouco mais simples. Você pode inverter quaisquer duas coordenadas para ver se isso também funciona para coordenadas que ainda não estão ordenadas (eu apenas testei a inversão A, Bmas deve funcionar para todas elas).

Eu não mudei nada \begin{document}e \end{document}ainda \Distanceestá lá, mas não o uso na minha definição de \DrawPotatoentão você realmente não precisa dele.

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,math}

% I don't use this in my \DrawPotato
\makeatletter % from https://tex.stackexchange.com/a/412901/121799
\newcommand{\Distance}[3]{% % from https://tex.stackexchange.com/q/56353/121799
    \tikz@scan@one@point\pgfutil@firstofone($#1-#2$)\relax  
    \pgfmathsetmacro{#3}{veclen(\the\pgf@x,\the\pgf@y)/28.45274}
}
\makeatother

\tikzset{
    declare function={
        interpolator(\x,\xmin,\xmax,\rmin,\rmax)=
            1/28.4527*((\rmin+\rmax)/2+((\rmin-\rmax)/2)*cos((\x-\xmin)*(180/(\xmax-\xmin))));
    }
}

\newcommand\DrawPotato[5][]{%
    \tikzmath{
        coordinate \p,\cent;
        \p0 = {(#2)};
        \p1 = {(#3)};
        \p2 = {(#4)};
        \p3 = {(#5)};
        \cent = ({(\px0+\px1+\px2+\px3)/4},{(\py0+\py1+\py2+\py3)/4}); % Average point
        real \angl,\dist;
        int \i,\j;
        for \i in {0,1,2,3}{
            \angl{\i} = atan2(\py{\i}-\centy,\px{\i}-\centx);
            \dist{\i} = veclen(\py{\i}-\centy,\px{\i}-\centx);
        };
        for \i in {0,1,2,3}{
            for \j in {0,1,2,3}{
                if min(\angl{0},\angl{1},\angl{2},\angl{3}) == \angl{\j} then {
                    \sortang{\i} = \angl{\j};
                    \sortind{\i} = \j;
                };
            };
            \angl{\sortind{\i}} = 500; % Arbitrary large value
            \sortdis{\i} = \dist{\sortind{\i}};
        };
    }
    \draw[#1,smooth,samples=50,shift={(\cent)}] 
        plot[variable=\x,domain=\sortang{0}:\sortang{1}] %
            (\x:{interpolator(\x,{\sortang{0}},{\sortang{1}},{\sortdis{0}},{\sortdis{1}})}) --
        plot[variable=\x,domain=\sortang{1}:\sortang{2}] %
            (\x:{interpolator(\x,{\sortang{1}},{\sortang{2}},{\sortdis{1}},{\sortdis{2}})}) --
        plot[variable=\x,domain=\sortang{2}:\sortang{3}] %
            (\x:{interpolator(\x,{\sortang{2}},{\sortang{3}},{\sortdis{2}},{\sortdis{3}})}) --
        plot[variable=\x,domain=\sortang{3}:\sortang{0}+360] %
            (\x:{interpolator(\x,{\sortang{3}},{\sortang{0}+360},{\sortdis{3}},{\sortdis{0}})}) --
        cycle ;
}

\begin{document}
\begin{frame}
\frametitle{What does the current code do?}
\begin{overlayarea}{\textwidth}{\textheight}
\begin{tikzpicture}
\path[use as bounding box] (-5,-3) rectangle (7,5);
\node[text width=8cm] (text) at (0,3){%
\only<1>{input: four points, here A, B, C \& D}
\only<2>{step one: compute the barycenter of those points}
\only<3>{imagine now a circle around the barycenter with radius equal to the 
average distance}
\only<4>{the code simply adds some sine functions to the radius such that the
contour runs through the points and the distance is extremal at those points}
\only<5>{however, the code is extremely clumsy and slow, and I have the feeling
that I'm re--inventing the wheel when dealing with lists etc.}
};
\coordinate (A) at (-1,1);
\coordinate (B) at (2,0.5);
\coordinate (C) at (4,-1);
\coordinate (D) at (1,-1);
\coordinate (Center) at (barycentric cs:A=1,B=1,C=1,D=1);
\pgfmathsetmacro{\TotalDistance}{0}
\xdef\DistanceList{}
\foreach \p in {A,B,C,D}
{\draw[fill=black] (\p) circle (1pt) node[below]{\p};
}
\Distance{(Center)}{(A)}{\DistanceA}
\Distance{(Center)}{(B)}{\DistanceB}
\Distance{(Center)}{(C)}{\DistanceC}
\Distance{(Center)}{(D)}{\DistanceD}
\pgfmathsetmacro{\AverageDistance}{(\DistanceA+\DistanceB+\DistanceC+\DistanceD)/4}
\pause
\draw[fill=black] (Center) circle (1pt) node[below]{Center};
\pause
\draw[-,dashed] (Center) circle (\AverageDistance);
\pause
\only<4->{
\DrawPotato[blue]{A}{B}{C}{D}
}
\end{tikzpicture}


\end{overlayarea}
\end{frame}
\end{document}

Answer 1

Com as bibliotecas mathe calc, é possível fazer isso de forma um pouco mais simples. Você pode inverter quaisquer duas coordenadas para ver se isso também funciona para coordenadas que ainda não estão ordenadas (eu apenas testei a inversão A, Bmas deve funcionar para todas elas).

Eu não mudei nada \begin{document}e \end{document}ainda \Distanceestá lá, mas não o uso na minha definição de \DrawPotatoentão você realmente não precisa dele.

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,math}

% I don't use this in my \DrawPotato
\makeatletter % from https://tex.stackexchange.com/a/412901/121799
\newcommand{\Distance}[3]{% % from https://tex.stackexchange.com/q/56353/121799
    \tikz@scan@one@point\pgfutil@firstofone($#1-#2$)\relax  
    \pgfmathsetmacro{#3}{veclen(\the\pgf@x,\the\pgf@y)/28.45274}
}
\makeatother

\tikzset{
    declare function={
        interpolator(\x,\xmin,\xmax,\rmin,\rmax)=
            1/28.4527*((\rmin+\rmax)/2+((\rmin-\rmax)/2)*cos((\x-\xmin)*(180/(\xmax-\xmin))));
    }
}

\newcommand\DrawPotato[5][]{%
    \tikzmath{
        coordinate \p,\cent;
        \p0 = {(#2)};
        \p1 = {(#3)};
        \p2 = {(#4)};
        \p3 = {(#5)};
        \cent = ({(\px0+\px1+\px2+\px3)/4},{(\py0+\py1+\py2+\py3)/4}); % Average point
        real \angl,\dist;
        int \i,\j;
        for \i in {0,1,2,3}{
            \angl{\i} = atan2(\py{\i}-\centy,\px{\i}-\centx);
            \dist{\i} = veclen(\py{\i}-\centy,\px{\i}-\centx);
        };
        for \i in {0,1,2,3}{
            for \j in {0,1,2,3}{
                if min(\angl{0},\angl{1},\angl{2},\angl{3}) == \angl{\j} then {
                    \sortang{\i} = \angl{\j};
                    \sortind{\i} = \j;
                };
            };
            \angl{\sortind{\i}} = 500; % Arbitrary large value
            \sortdis{\i} = \dist{\sortind{\i}};
        };
    }
    \draw[#1,smooth,samples=50,shift={(\cent)}] 
        plot[variable=\x,domain=\sortang{0}:\sortang{1}] %
            (\x:{interpolator(\x,{\sortang{0}},{\sortang{1}},{\sortdis{0}},{\sortdis{1}})}) --
        plot[variable=\x,domain=\sortang{1}:\sortang{2}] %
            (\x:{interpolator(\x,{\sortang{1}},{\sortang{2}},{\sortdis{1}},{\sortdis{2}})}) --
        plot[variable=\x,domain=\sortang{2}:\sortang{3}] %
            (\x:{interpolator(\x,{\sortang{2}},{\sortang{3}},{\sortdis{2}},{\sortdis{3}})}) --
        plot[variable=\x,domain=\sortang{3}:\sortang{0}+360] %
            (\x:{interpolator(\x,{\sortang{3}},{\sortang{0}+360},{\sortdis{3}},{\sortdis{0}})}) --
        cycle ;
}

\begin{document}
\begin{frame}
\frametitle{What does the current code do?}
\begin{overlayarea}{\textwidth}{\textheight}
\begin{tikzpicture}
\path[use as bounding box] (-5,-3) rectangle (7,5);
\node[text width=8cm] (text) at (0,3){%
\only<1>{input: four points, here A, B, C \& D}
\only<2>{step one: compute the barycenter of those points}
\only<3>{imagine now a circle around the barycenter with radius equal to the 
average distance}
\only<4>{the code simply adds some sine functions to the radius such that the
contour runs through the points and the distance is extremal at those points}
\only<5>{however, the code is extremely clumsy and slow, and I have the feeling
that I'm re--inventing the wheel when dealing with lists etc.}
};
\coordinate (A) at (-1,1);
\coordinate (B) at (2,0.5);
\coordinate (C) at (4,-1);
\coordinate (D) at (1,-1);
\coordinate (Center) at (barycentric cs:A=1,B=1,C=1,D=1);
\pgfmathsetmacro{\TotalDistance}{0}
\xdef\DistanceList{}
\foreach \p in {A,B,C,D}
{\draw[fill=black] (\p) circle (1pt) node[below]{\p};
}
\Distance{(Center)}{(A)}{\DistanceA}
\Distance{(Center)}{(B)}{\DistanceB}
\Distance{(Center)}{(C)}{\DistanceC}
\Distance{(Center)}{(D)}{\DistanceD}
\pgfmathsetmacro{\AverageDistance}{(\DistanceA+\DistanceB+\DistanceC+\DistanceD)/4}
\pause
\draw[fill=black] (Center) circle (1pt) node[below]{Center};
\pause
\draw[-,dashed] (Center) circle (\AverageDistance);
\pause
\only<4->{
\DrawPotato[blue]{A}{B}{C}{D}
}
\end{tikzpicture}


\end{overlayarea}
\end{frame}
\end{document}

Melhorando batatas TikZ

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