Verbesserung von TikZ-Kartoffeln

Question

Mit den Bibliotheken mathund calcist es möglich, es etwas einfacher zu machen. Sie können zwei beliebige Koordinaten umdrehen, um zu sehen, ob es auch für Koordinaten funktioniert, die noch nicht geordnet sind (ich habe nur das Umdrehen Aund getestet, Baber es sollte für alle funktionieren).

Ich habe zwischendurch nichts geändert \begin{document}und \end{document}„sodass“ \Distanceist immer noch da, aber ich verwende es nicht in meiner Definition von „ \DrawPotatosodass Sie es nicht wirklich brauchen“.

\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

Mit den Bibliotheken mathund calcist es möglich, es etwas einfacher zu machen. Sie können zwei beliebige Koordinaten umdrehen, um zu sehen, ob es auch für Koordinaten funktioniert, die noch nicht geordnet sind (ich habe nur das Umdrehen Aund getestet, Baber es sollte für alle funktionieren).

Ich habe zwischendurch nichts geändert \begin{document}und \end{document}„sodass“ \Distanceist immer noch da, aber ich verwende es nicht in meiner Definition von „ \DrawPotatosodass Sie es nicht wirklich brauchen“.

\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}

Verbesserung von TikZ-Kartoffeln

Antwort1

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