[Tex/LaTex] Tikz Nodes Positions and Shapes with a General Number of Nodes

tikz-pgftikz-styles

My purpose is rather simple: use tikzpictures to draw tables of numbers, where the numbers are drawn inside colored boxes with fancy shapes, with different shapes and colors for different numbers. Below I boxed numbers according to whether they were odd, even, or prime (and treated 1 as a special number).

The idea is to use the colors and shapes to spot patterns. My original plan was to use this to teach prime numbers, but I have since thought of other things that could be fun to do.

As I'm new to tikz (a few days on it only), there are still some basic things that are eluding me. Here are the improvements and alterations I'd like to make on the basic table displayed below.

Resize the shapes to approximately the same "size"

There are several interpretations of what that might mean, any reasonable one will be fine. Right now, the boxes adapt to the size of the numbers, with single-digit numbers having small boxes, two-digit numbers larger boxes, and three-digit numbers even larger. I'd like the numbers to shrink rather than the boxes. You can also see that I had trouble getting the star shape to align with the other shapes. I did fool around with anchor, inner sep and outer sep, but that's all I know of at this time.
Control the direction in which the numbers are running

I am asking this as a separate question, by popular demand: Tikz Nodes Order and Shapes with a General Number of Nodes

To be clear, I will be generating tables of different sizes, some with 10 numbers, some with 100 numbers, possibly more, some with longer rows, some with longer columns, and I'd like the shapes to resize automatically and proportionately.

I haven't thought through the choice of shapes and colors, it's a first pass. Feel free to beautify 😉

This is the code so far:

\RequirePackage[svgnames,x11names]{xcolor}
\documentclass[tikz,convert=false,margin=0pt]{standalone}%
\usetikzlibrary{shapes.geometric}% polygon, ellipse, star, diamond, etc.
\usepackage{tkz-euclide}% \pgfmathisprime command
\usepackage{rotating}% sideways environment

\begin{document}%
\begin{tikzpicture}[%
  every node/.style = {
    shape = circle
    , align = center
    , scale = 2
    , anchor = base
    , font = \fontfamily{pzc}\selectfont% common font
  } ,
  % Prime Numbers
  PrimeStyle/.style = {
    regular polygon
    , regular polygon sides = 3
    , rounded corners = .5em
    , inner sep = 0pt 
    , outer sep = 0pt
    , draw = DarkGreen, thick
    , fill = green!70!black
    , text = white
  } ,
  % Even Numbers 
  EvenStyle/.style = {
    shape = circle
    , inner sep = 2pt
    , draw = DarkRed, thick
    , fill = red!70!black
    , text = white
  } ,
  % Non-Prime Odd Numbers
  OddStyle/.style = {
    shape = diamond
    , rounded corners = .5em
    , inner sep = 1pt
    , draw = DarkBlue, thick
    , fill = blue!70!black
    , text = white
  } , 
  % Number One
  OneStyle/.style = {
    shape = star
    , rounded corners = .5em
    , inner sep = 2pt
    , scale = 0.9
    , draw = white!70!black, thick
    , fill = blue!50!green!50!
    , text = black
  }
]%
%
  % Set Grid Dimensions 
  \newcommand{\xa}{1}
  \newcommand{\xb}{10}
  \newcommand{\ya}{1}
  \newcommand{\yb}{10}
  \pgfmathsetmacro{\yc}{\yb-1}% \yb minus one
% 
  % Change styles of numbers according to set membership
  \foreach \x in {\xa,...,\xb}
    \foreach \y in {\ya,...,\yb} 
       {\pgfmathtruncatemacro{\label}{\x - \xb * (\y - \yb) }
         \pgfmathparse{int(mod(\label,2))}
         \let \r \pgfmathresult
         \ifnum \r = 1
           \tikzset{EvenStyle/.style = {OddStyle}}
         \fi
         \pgfmathisprime{int(\label)}
         \let \s \pgfmathresult
         \ifnum \s = 1
           \tikzset{EvenStyle/.style = {PrimeStyle}}
         \fi
         \pgfmathparse{int(\label)}
         \let \t \pgfmathresult
         \ifnum \t = 1
           \tikzset{EvenStyle/.style = {OneStyle}}
         \fi
         \node [EvenStyle]  (\x\y) at (1.5*\x, -1.5*\y) {\label};} 
  \foreach \x in {\xa,...,\xb}
    \foreach \y [count = \yi] in {\ya,...,\yc}
      \draw (\x\y)(\x\yi) (\y\x)(\yi\x) ;
\end{tikzpicture}%
\end{document}%

% doesn't work, why?
% \foreach \k in {1,2,3,5,7,11,13}
%  \tikzset{EvenStyle/.style = {PrimeStyle}} ;

This is the immediate predecessor to this question:
Looking for Elegance and Convenience in Code with Many Numbers
where Harish Kumar showed me how to write general code using foreach loops.

This is where I learned of a slightly different way of defining the grid:
Selecting specific nodes and changing style (for those nodes)

This is where I learned about the \pgfmathisprime command from the tikz-euler package:
How to produce a list of prime numbers in LaTeX

Here I saw one of several examples where I learned how to use ifnum with int and mod and \pgfmathparse :
How to use mod operation in latex with tikz

enter image description here

Best Answer

I'm not sure if it's answering all your questions, but I think the following (although not perfect) shows some ways in which your code could be simplified. I think there will always be some manual adjustment involved though (e.g., setting appropriate inner sep).

\documentclass[tikz,border=0.125cm]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}
\tikzset{%
  set color/.style={
    fill=#1,
    draw=#1!50!black
  },
  every number/.style={
    text=white,
    rounded corners=0.125cm,
    font=\fontfamily{pzc}\selectfont,
    text width=3ex,
    align=center,
    scale=2
  },
  every prime number/.style={
    shape=diamond,
    set color=blue!70!black,
    inner sep=0.25ex,
  },
  every even number/.style={
    shape=circle,
    set color=red!70!black,
    inner sep=0.5ex
  },
  every odd number/.style={
    shape=regular polygon,
    regular polygon sides=3,
    set color=green!70!black,
    inner sep=-0.375ex
  },
  number 1/.style={
    shape=star,
    set color=green!50!blue,
    inner sep=-.25ex
  }
}%
\begin{tikzpicture}[x=2cm, y=2cm]
\foreach \n [evaluate={%
    \x=mod(\n-1,10); 
    \y=floor((\n-1)/10);
    \p=isprime(\n);
    \e=mod(\n,2)==0;
    \style=(\p || \n==2) ? "prime" : (\e ? "even" : "odd");}] in {1,...,100}
  \node [every number/.try, every \style\space number/.try, number \n/.try]
     at (\x,\y) {\n};
\end{tikzpicture}

\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

The source of the difficulty is that ellipses are constructed in a particular way in TikZ. They are paths that start from the x-axis and proceed counter-clockwise around their centre. The vast majority of the time, the exact parametrisation doesn't matter. You appear to have found the one situation where it does!

In the actual question, you only want to be able to mirror the ellipse, and so draw it starting from the negative x-axis (the title of the question suggests a more flexible approach). That's actually not too hard since we can exploit the symmetry of the ellipse. The key is to provide it with a negative x-radius, since then it will start from the negative x-axis (and proceed clockwise, but we could correct for that by negating the y-radius as well). To do this, we interrupt the call from the node shape to the drawing command and flip the sign of the x-radius. The simplest way to do this is to redefine the \pgfpathellipse macro to do the negation and then call the original macro. The following code does this.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations,shapes,decorations.markings}
\makeatletter
\let\origpgfpathellipse=\pgfpathellipse
\def\revpgfpathellipse#1#2#3{%
  #2%
  \pgf@xa=-\pgf@x
  \origpgfpathellipse{#1}{\pgfqpoint{\pgf@xa}{0pt}}{#3}}
\makeatother

\tikzset{
  reversed ellipse/.style={
    ellipse,
    reverse the ellipse%
  },
  reverse the ellipse/.code={
    \let\pgfpathellipse=\revpgfpathellipse
  }
}
\begin{document}
\begin{tikzpicture}
\node[ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,0) {hello world};

\node[reversed ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,-2) {hello world};
\end{tikzpicture}

\end{document}

Here's the result:

rotated ellipse

(the arrow got clipped, but you can see where it lies)

[Tex/LaTex] defining a region to fill in a tikz shape

TikZ doesn't allow you to apply the fill and draw commands to separate pieces of a path. The relevant part is in the macro \tikz@finish. On a normal path, the drawing and filling is done by the piece:

  \edef\tikz@temp{\noexpand\pgfusepath{%
    \iftikz@mode@fill fill,\fi%
    \iftikz@mode@draw draw,\fi%
    \iftikz@mode@clip clip,\fi%
    }}%
  \tikz@temp%

In a node shape, the \backgroundpath is the path used at this point. Now you don't want this: you want to be able to specify part of the \backgroundpath as for draw and part for fill. So you have to specify two paths. Neither can actually be in place at the point where TikZ normally draws or fills since neither should have both actions applied. Normally, I'd recommend using the fact that a node shape can have several paths associated to it (\beforebackgroundpath and so forth), but then you get into complications with passing styles to the different parts (in the TQFT package I use this to style the various parts of a cobordism, but there it is reasonable as there are different components. Here you just have one thing and splitting it is less user-friendly.).

So we just need to subvert the normal TikZ mechanism and replace it with our own. This means using the \backgroundpath at definition time rather than leaving it to later. You do this already in the hackgenuspic (and other) shapes. The only bit you don't do is use it conditionally.

At the time that the \backgroundpath is processed, all of TikZ's path options have been processed. So TikZ knows the fill colour, the line width, the draw colour, and so forth. The only bit it doesn't know is whether or not to fill or draw the path. This is only figured out at the finish. (This is reasonable: the definition of the path can depend on the options, but doesn't usually depend on the action to be taken.) Fortunately, it isn't hard to find out what the desired actions are: we simply execute \tikz@mode. This sets a few conditionals, namely \iftikz@mode@fill and \iftikz@mode@draw (there's also \iftikz@mode@clip and a few more - for a truly robust solution we should consider them as well).

And from that, the rest is fairly easy. We execute \tikz@mode and if we need to fill the path, we define and fill the hole, and if we need to draw it, we define and draw the outer part. Given that we're using \tikz@mode a little earlier than usual, I've put it inside a group. I suspect I'm just being overcautious on this, though, as TikZ is fairly careful about not making assumptions.

Here's my code. The shape is based on hackgenuspic (but I renamed it to just genus). It's quite likely that I've missed something - I haven't stress-tested it! Please let me know if it breaks. (If not, it would seem a reasonable addition to the TQFT package - what do you think?)

\documentclass[convert]{standalone}
%\documentclass{article}
\usepackage{tikz, pgf}
\usetikzlibrary{shapes}

\makeatletter

\pgfdeclareshape{genus}{
 \anchor{center}{\pgfpointorigin}
\backgroundpath{
    \begingroup
    \tikz@mode
    \iftikz@mode@fill

         \pgfpathmoveto{\pgfqpoint{-0.78cm}{-.17cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.35cm}{-.44cm}}
        {\pgfpoint{0.35cm}{-.44cm}}
        {\pgfpoint{.78cm}{-0.17cm}} 
     \pgfpathmoveto{\pgfqpoint{-0.78cm}{-0.17cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.25cm}{.25cm}}
        {\pgfpoint{.25cm}{.25cm}}
        {\pgfpoint{0.78cm}{-0.17cm}}
        \pgfusepath{fill}
        \fi

        \iftikz@mode@draw
     \pgfpathmoveto{\pgfqpoint{-1cm}{0cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.5cm}{-.5cm}}
        {\pgfpoint{0.5cm}{-.5cm}}
        {\pgfpoint{1cm}{0cm}}

     \pgfpathmoveto{\pgfqpoint{-0.75cm}{-0.15cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.25cm}{.25cm}}
        {\pgfpoint{.25cm}{.25cm}}
        {\pgfpoint{0.75cm}{-0.15cm}}
              \pgfusepath{stroke}
        \fi
        \endgroup
    }
    }

    \makeatother

\begin{document}
\begin{tikzpicture}[scale=.5]
\fill[color=black!10] (-6,3) arc (-180:0:2 cm and 1 cm) 
 (-2,3) .. controls +(-60:1) and +(-120:1) .. (2,3)
(2,3)  arc (-180:0:2 cm and 1 cm)
(6,3) .. controls +(-90:2) and +(0:4) .. (0,-10) .. controls +(180:4) and +(-90:2) .. (-6,3);

\node [genus, scale=1, fill=green] at (0,0) {};
\node [genus, draw, scale=1, fill=orange] at (0,-2) {};
\node [genus, draw, ultra thick, scale=1, fill=green] at (0, -4) {};
\node [genus, draw, scale=.7] at (0, -6) {};
\node [genus, draw, dashed, scale=.5, fill=green] at (0, -8) {};


\draw (-4,3) ellipse (2 cm and 1 cm) 
 (-2,3) .. controls +(-60:1) and +(-120:1) .. (2,3)
(4,3)  ellipse (2cm and 1cm)
(6,3) .. controls +(-90:2) and +(0:4) .. (0,-10) .. controls +(180:4) and +(-90:2) .. (-6,3);
\end{tikzpicture}
\end{document}

with result:

Riemann surface with genus

Best Answer

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

[Tex/LaTex] defining a region to fill in a tikz shape

Related Question