[Tex/LaTex] Pascal’s triangle in Tikz with symbols

tikz-pgf

I have a follow-up question to Pascal's triangle in tikz with row headers.

Is it possible to produce Mark's solution with symbols in Pascal's triangle? So, I could create the same figure, but instead of numbers, I would generate Pascal's triangle with ${\n \choose \k}$ at each node.

Thanks!

Best Answer

Load the amsmath package to enable \binom{}{}.

Making use of this answer here

\documentclass[tikz,border=5]{standalone}
\usepackage{amsmath}
\usepgflibrary{fpu}
\begin{document}
\def\N{10}
\tikz[x=0.75cm,y=0.5cm, 
  pascal node/.style={font=\footnotesize}, 
  row node/.style={font=\footnotesize, anchor=west, shift=(180:1)}]
  \path  
    \foreach \n in {0,...,\N} { 
      (-\N/2-1, -\n) node  [row node/.try]{Row \n:}
        \foreach \k in {0,...,\n}{
          (-\n/2+\k,-\n) node [pascal node/.try] {%
%            \pgfkeys{/pgf/fpu}%
%            \pgfmathparse{round(\n!/(\k!*(\n-\k)!))}%
%            \pgfmathfloattoint{\pgfmathresult}%
%            \pgfmathresult%
             $\binom{\n}{\k}$  
        }}};
\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Pascal’s triangle in tikz with row headers

The following should do it. By using the fpu library it is possible to go beyond the usual limit of 17 rows in PGF.

\documentclass[tikz,border=5]{standalone}
\usepgflibrary{fpu}
\begin{document}
\def\N{10}
\tikz[x=0.75cm,y=0.5cm, 
  pascal node/.style={font=\footnotesize}, 
  row node/.style={font=\footnotesize, anchor=west, shift=(180:1)}]
  \path  
    \foreach \n in {0,...,\N} { 
      (-\N/2-1, -\n) node  [row node/.try]{Row \n:}
        \foreach \k in {0,...,\n}{
          (-\n/2+\k,-\n) node [pascal node/.try] {%
            \pgfkeys{/pgf/fpu}%
            \pgfmathparse{round(\n!/(\k!*(\n-\k)!))}%
            \pgfmathfloattoint{\pgfmathresult}%
            \pgfmathresult%
          }}};
\end{document}

enter image description here

[Tex/LaTex] How to draw small a triangle mesh using tikz

I'm a beginner at tikz and I just developed this on the fly, so it is not pretty. I also included a lot of diagnostic text so as to help you follow my logic.

It takes a node file that provides node numbers and their coordinates.

And an element file that gives an element number and the nodes that make up the connectivity of the element. Doesn't matter if they are triangles or quads, or something else.

The macro \drawmesh, used inside a tikzpicture creates the string of \draws to formulate the mesh. Note numbers, coordinates, element connectivity are all stored in accessible, expandable arrays \noddat[row,col] and \eledat[row,col].

EDITED to add the macro \labelnodes.

EDITED to add the macro \labelelements.

EDITED to allow for either file input or manual input of node and element data. The file input approach would look like this:

\begin{filecontents*}{nodedata.dat}
1  0.000  0.000
2  1.000  0.000
3  2.000  0.500
4  0.000  1.000
5  1.000  1.000
6  1.750  1.300
7  2.700  0.800
8  2.300  1.700
\end{filecontents*}
\begin{filecontents*}{elementdata.dat}
1  1  2  5
2  5  4  1
3  2  3  6
4  6  5  2
5  3  7  8  6
\end{filecontents*}
\readmesh{nodedata.dat}{elementdata.dat}

The manual input approach like this:

\def\nodedata{1 0.000 0.000,2 1.000 0.000,3 2.000 0.500,
4 0.000 1.000,5 1.000 1.000,6 1.750 1.300,7 2.700 0.800,8 2.300 1.700}
\def\elementdata{1 1 2 5,2 5 4 1,3 2 3 6,4 6 5 2,5 3 7 8 6}
\readmesh{}{}

EDITED to allow several alternatives for \labelnode appearance

EDITED to allow LaTeX style labels for nodes and elements, rather than just numbers.

The MWE:

\documentclass{article}
\usepackage{tikz,listofitems,readarray,filecontents}
\usetikzlibrary{calc}
\begin{filecontents*}{nodedata.dat}
1  0.000  0.000
2  1.000  0.000
3  2.000  0.500
4  0.000  1.000
5  1.000  1.000
6  1.750  1.300
7  2.700  0.800
n_8  2.300  1.700
\end{filecontents*}
\begin{filecontents*}{elementdata.dat}
E_1  1  2  5
2  5  4  1
3  2  3  6
4  6  5  2
5  3  7  n_8  6
\end{filecontents*}

\newcommand\coord[2][]{%
  \edef\comparenode{#2}%
  \foreachitem\zzz\in\noddat[]{%
    \edef\testnode{\noddat[\zzzcnt,1]}%
    \ifx\testnode\comparenode
      \xaddtomacro\tmp{(\noddat[\zzzcnt,2]#1,\noddat[\zzzcnt,3]#1)}\fi
  }%
}

\makeatletter\let\addtomacro\g@addto@macro\makeatother
\newcommand\xaddtomacro[2]{%
  \edef\xtmp{#2}%
  \expandafter\addtomacro\expandafter#1\expandafter{\xtmp}%
}

\newcommand\drawmesh[1][\draw]{%
  \def\tmp{}%
  \foreachitem\z\in\eledat[]{%
    \addtomacro\tmp{#1}%
    \foreachitem\zz\in\eledat[\zcnt]{%
      \ifnum\zzcnt=1\relax\else
        \ifnum\zzcnt<\listlen\eledat[\zcnt]\relax
          \ifnum\zzcnt=2\relax\coord{\zz}\fi
          \addtomacro\tmp{--}%
          \coord{\eledat[\zcnt,\the\numexpr\zzcnt+1\relax]}%
        \else
          \addtomacro\tmp{--}%
          \coord{\eledat[\zcnt,2]}%
        \fi
      \fi
    }%
    \addtomacro\tmp{;}%
  }%
  \tmp%
}

\newcommand\labelnodes[1][\node at]{%
  \foreachitem\z\in\noddat[]{%
    #1 (\noddat[\zcnt,2],\noddat[\zcnt,3]){%
%% ALTERNATIVE 1
%      \textcolor{red}{$\noddat[\zcnt,1]$}};
%% ALTERNATIVE 2
      \fboxsep=0pt\relax
      \colorbox{white}{\color{red}$\noddat[\zcnt,1]$}};
%%
  }%
}

\newcommand\labelelements[1][\node at]{%
  \foreachitem\z\in\eledat[]{%
    \def\tmp{#1 }%
    \addtomacro\tmp{($}
    \foreachitem\zz\in\eledat[\zcnt]{%
      \ifnum\zzcnt=1\relax\else
        \ifnum\zzcnt=2\relax\else\addtomacro\tmp{ + }\fi%
        \coord[{/\the\numexpr\listlen\eledat[\zcnt]-1\relax}]{%
          \eledat[\zcnt,\zzcnt]}%
      \fi
    }%
    \addtomacro\tmp{$)}%
    \xaddtomacro\tmp{{\noexpand\textcolor{blue!70!green}{$\eledat[\zcnt,1]$}};}%
   \tmp
  }%
}

\newcommand\readmesh[2]{%
  \ignoreemptyitems%
  \readarraysepchar{,}%
  \ifx\relax#1\relax\else\readdef{#1}\nodedata\fi
  \ifx\relax#2\relax\else\readdef{#2}\elementdata\fi
  \setsepchar{,/ }%
  \readlist*\noddat{\nodedata}%
  \readlist*\eledat{\elementdata}%
}
\begin{document}
%% FILE INPUT
\readmesh{nodedata.dat}{elementdata.dat}

%% OR MANUAL INPUT
%\def\nodedata{1 0.000 0.000,2 1.000 0.000,3 2.000 0.500,
%4 0.000 1.000,5 1.000 1.000,6 1.750 1.300,7 2.700 0.800,n_8 2.300 1.700}
%\def\elementdata{E_1 1 2 5,2 5 4 1,3 2 3 6,4 6 5 2,5 3 7 n_8 6}
%\readmesh{}{}

Selected data extracts: \eledat[3,3], \noddat[3,3]

Segment list in terms of node numbers:\\
\foreachitem\z\in\eledat[]{%
  Element $\eledat[\zcnt,1]$:
  \foreachitem\zz\in\eledat[\zcnt]{%
    \ifnum\zzcnt=1\relax\else
      \ifnum\zzcnt<\listlen\eledat[\zcnt]\relax
        $\zz$--$\eledat[\zcnt,\the\numexpr\zzcnt+1\relax]$,
      \else
        $\zz$--$\eledat[\zcnt,2]$
      \fi
    \fi
  }%
  \\
}

Segment list in terms of node coordinates:\\
\drawmesh[draw]

\begin{figure}[ht]
\centering
\begin{tikzpicture}[scale=1.5]
  \drawmesh
  \labelnodes
  \labelelements
\end{tikzpicture}
\caption{A finite element mesh}
\end{figure}
\end{document}

Without all the diagnostic stuff included, and choosing manual over file input as the mode of input, the code is a bit more streamlined

\documentclass{article}
\usepackage{tikz,listofitems,readarray}
\usetikzlibrary{calc}
\newcommand\coord[2][]{%
  \edef\comparenode{#2}%
  \foreachitem\zzz\in\noddat[]{%
    \edef\testnode{\noddat[\zzzcnt,1]}%
    \ifx\testnode\comparenode
      \xaddtomacro\tmp{(\noddat[\zzzcnt,2]#1,\noddat[\zzzcnt,3]#1)}\fi
  }%
}
\makeatletter\let\addtomacro\g@addto@macro\makeatother
\newcommand\xaddtomacro[2]{%
  \edef\xtmp{#2}%
  \expandafter\addtomacro\expandafter#1\expandafter{\xtmp}%
}
\newcommand\drawmesh[1][\draw]{%
  \def\tmp{}%
  \foreachitem\z\in\eledat[]{%
    \addtomacro\tmp{#1}%
    \foreachitem\zz\in\eledat[\zcnt]{%
      \ifnum\zzcnt=1\relax\else
        \ifnum\zzcnt<\listlen\eledat[\zcnt]\relax
          \ifnum\zzcnt=2\relax\coord{\zz}\fi
          \addtomacro\tmp{--}%
          \coord{\eledat[\zcnt,\the\numexpr\zzcnt+1\relax]}%
        \else
          \addtomacro\tmp{--}%
          \coord{\eledat[\zcnt,2]}%
        \fi
      \fi
    }%
    \addtomacro\tmp{;}%
  }%
  \tmp%
}
\newcommand\labelnodes[1][\node at]{%
  \foreachitem\z\in\noddat[]{%
    #1 (\noddat[\zcnt,2],\noddat[\zcnt,3]){%
      \fboxsep=0pt\relax
      \colorbox{white}{\color{red}$\noddat[\zcnt,1]$}};
  }%
}
\newcommand\labelelements[1][\node at]{%
  \foreachitem\z\in\eledat[]{%
    \def\tmp{#1 }%
    \addtomacro\tmp{($}
    \foreachitem\zz\in\eledat[\zcnt]{%
      \ifnum\zzcnt=1\relax\else
        \ifnum\zzcnt=2\relax\else\addtomacro\tmp{ + }\fi%
        \coord[{/\the\numexpr\listlen\eledat[\zcnt]-1\relax}]{%
          \eledat[\zcnt,\zzcnt]}%
      \fi
    }%
    \addtomacro\tmp{$)}%
    \xaddtomacro\tmp{{\noexpand\textcolor{blue!70!green}{$\eledat[\zcnt,1]$}};}%
   \tmp
  }%
}
\newcommand\readmesh[2]{%
  \ignoreemptyitems%
  \readarraysepchar{,}%
  \ifx\relax#1\relax\else\readdef{#1}\nodedata\fi
  \ifx\relax#2\relax\else\readdef{#2}\elementdata\fi
  \setsepchar{,/ }%
  \readlist*\noddat{\nodedata}%
  \readlist*\eledat{\elementdata}%
}
\begin{document}
\def\nodedata{1 0.000 0.000,2 1.000 0.000,3 2.000 0.500,
4 0.000 1.000,5 1.000 1.000,6 1.750 1.300,7 2.700 0.800,n_8 2.300 1.700}
\def\elementdata{E_1 1 2 5,2 5 4 1,3 2 3 6,4 6 5 2,5 3 7 n_8 6}
\readmesh{}{}
\begin{figure}[ht]
\centering
\begin{tikzpicture}[scale=1.5]
  \drawmesh
  \labelnodes
  \labelelements
\end{tikzpicture}
\caption{A finite element mesh}
\end{figure}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Pascal’s triangle in tikz with row headers

[Tex/LaTex] How to draw small a triangle mesh using tikz

Related Question