TikZ PGF – How to Draw a Convex Hull with TikZ in LaTeX

tikz-pgf

I want to draw a convex hull with tikz.

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{center}
\begin{tikzpicture}

\def\us{(0,2),(1,4),(2,0),(3,2),(4,1),(6,2),(6,4)}

\foreach \u [count=\i from 1] in \us {\node (u\i) at \u [right] {$u_\i$};}

\fill[fill=blue] (u1) -- (u2) -- (u3);
% \fill[red] (0,2) -- (2,0) -- (3,2);

\end{tikzpicture}
\end{center}

\end{document}

If I'm right, this should draw a filled blue triangle.
But it doesn't! Why? If instead, I comment out the \fill[red] line, I do see a result.

Thank you, Adrian.

Best Answer

This is because TikZ automatically uses the most appropriate anchor to connect two nodes, so you do not actually have a triangle, you have two edges.

Try

\fill[fill=blue] (u1.center) -- (u2.center) -- (u3.center) ;

instead, it will show the difference.

Other ways are to use

\def\us{0/2,1/4,2/0,3/2,4/1,6/2,6/4}
\foreach \x/\y [count=\i from 1] in \us {
   \coordinate[label=right:$u_\i$] (u\i) at (\x,\y);
}

instead, as coordinates are automatically connected using their "center" anchor.

Finally, a more sophisticated way might be this one:

\def\us{(0,2)/left,(1,4)/right,(2,0)/right,
   (3,2)/above,(4,1)/above,(6,2)/below,(6,4)/below}

\foreach \u/\pos [count=\i from 1] in \us {
   \node[shape=coordinate,label=\pos:$u_\i$] (u\i) at \u {};
}

This gives you the possibility to set the label position individually for each coordinate so that they are not interfering with connecting lines etc.

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[Tex/LaTex] Numerical conditional within tikz keys

I am definitely unfamiliar with both beamer and tikz (do not quite get what the \only are supposed to do) but perhaps this could go in the direction you want:

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{chains}
\newcounter{count}

% helper macro:
\long\def\GobToSemiColon #1;{}

\newcommand\myPicture{
\begin{tikzpicture}
  \begin{scope}[start chain = going below]
  \ifnum\value{count}<1 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>3 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is between
    1 and 3};

  \ifnum\value{count}>-1 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is
    negative}; 

  \ifnum\value{count}<100 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>200 \expandafter\GobToSemiColon\fi  
  \node[draw, rectangle, on chain] {display only if counter is between
    100 and 200};

  \ifnum\value{count}<3 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>20 \expandafter\GobToSemiColon\fi
  \node[draw, circle, on chain] {only when counter is in the range 3 to 20};
  \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{frame}
\only{\setcounter{count}{-3}\myPicture}
\only{\setcounter{count}{105}\myPicture}
\only{\setcounter{count}{39}\myPicture}
\only{\setcounter{count}{2}\myPicture}
\only{\setcounter{count}{5}\myPicture}
\end{frame}
\end{document}

beamer

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Numerical conditional within tikz keys

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

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