TikZ: rotating a pic of nodes

Question

A friend showed a quilt pattern on which they were working. Ah, I said, I could easily do that in TikZ with pics. Well, yes and no: Do it, certainly; easily, not so much. I have the pic shown below, as well as the finished pattern which was done completely by brute force. There must be a way to do this more efficiently, and in a way that could be generalized for other patters.

\documentclass{article}

\usepackage[papersize={5.5in,8.5in},margin=0.6in]{geometry}
\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\tikzset{%
    dartstyle/.style={kite,draw,kite vertex angles=60,inner sep=0.125in,outer sep=0pt,fill=#1},
    pics/quiltdart/.style={%
        code={%
          \node[dartstyle=red](base) {};
          \node[rotate=0,dartstyle=white,anchor=upper vertex] at (base.right vertex) {};
          \node[rotate=0,dartstyle=white,anchor=upper vertex] at (base.left vertex) {};
          \node[rotate=0,dartstyle=red,anchor=upper vertex] at (base.lower vertex) {};
        }%
    }%
}

\parindent0pt

\begin{document}

This was easy:

\tikz \pic {quiltdart};

\bigskip

This, not so much\dots

\tikz {\pic {quiltdart};
    \pic[yshift=-0.51in,xshift=0.89in,rotate=-60,transform shape]  {quiltdart};
    \pic[yshift=-1.54in,xshift=0.89in,rotate=-120,transform shape]  {quiltdart};
    \pic[yshift=-2.05in,xshift=-0in,rotate=-180,transform shape]  {quiltdart};
    \pic[yshift=-1.54in,xshift=-0.89in,rotate=-240,transform shape]  {quiltdart};
    \pic[yshift=-0.51in,xshift=-0.89in,rotate=-300,transform shape]  {quiltdart};
}

\end{document}

Update

First, I want to thank those who have replied to my post: I have learned an enormous amount. For that reason, I am posting this as an Update rather than an Answer because it would not have been possible without the thought-provoking replies from which I do not in any way wish to detract.

Here is my approach. It works nicely though it is probably not the most efficient code possible. On the other hand it is straightforward and easily maintained/tinkered-with.

\documentclass[]{article}

\usepackage[rgb]{xcolor}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage[margin=1.4in,top=0.5in,left=0.75in]{geometry}

\NewDocumentCommand{\makeshape}{m}{%
    \pgfmathsetmacro{\myhuei}{rnd}
    \pgfmathsetmacro{\myhueii}{rnd}
    \pgfmathsetmacro{\myhueiii}{rnd}
    \definecolor{mycolori}{hsb}{\myhuei,1,1}
    \definecolor{mycolorii}{hsb}{\myhueii,0.25,1}
    \definecolor{mycoloriii}{hsb}{\myhueiii,1,1}
    \pgfmathsetmacro{\lang}{180/#1}%
    \pgfmathsetmacro{\bang}{90-\lang}%
    \tikzset{%
        pics/dart/.style={code={%
            \draw[fill=mycolorii] (0,0) -- ++(90-\lang:2) --
                ++(180-\bang:2) -- ++(-90-\lang:2) -- cycle;
            \draw[fill=mycolori](0,0) -- ++(90-\lang:1) -- ++(180 - \bang:1)coordinate(T) --
                ++(-90-\lang:1) -- cycle;
            \draw[fill=mycoloriii](T) -- ++(90-\lang:1) -- ++(-180 - \bang:1) --
                ++(-90-\lang:1)-- cycle;
            }%
        },%
    }%
    \begin{tikzpicture}[rotate=\lang,scale=0.5]%% both rotate and scale can be altered to suit
        \foreach \i [count=\ii from 0] in {1,...,#1}
            \path pic[rotate around={360/#1*\ii:(0,0)},transform shape]{dart};
    \end{tikzpicture}
}

\parindent0pt

\begin{document}

\thispagestyle{empty}

\foreach \N in {4,5,...,18}{\makeshape{\N}}

\end{document}

Answer 1

Here is a somewhat improvement by using a \foreach statement and replacing the rotate option by rotate around.

\documentclass{article}

\usepackage[papersize={5.5in,8.5in},margin=0.6in]{geometry}
\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\tikzset{%
    dartstyle/.style={kite,draw,kite vertex angles=60,inner sep=0.125in,outer sep=0pt,fill=#1},
    pics/quiltdart/.style={%
        code={%
          \node[dartstyle=red](base) {};
          \node[rotate=0,dartstyle=white,anchor=upper vertex] at (base.right vertex) {};
          \node[rotate=0,dartstyle=white,anchor=upper vertex] at (base.left vertex) {};
          \node[rotate=0,dartstyle=red,anchor=upper vertex] 
                at (base.lower vertex)(bottom dart){}; % <-----
        }%
    }%
}

\parindent0pt

\begin{document}

This was easy:

\tikz \pic {quiltdart};

\bigskip

What about this ???


\begin{tikzpicture}
 \foreach \i in {0,60,...,300}{
  \pic[rotate around={\i:(bottom dart.lower vertex)},
      transform shape] {quiltdart};
  }

\end{tikzpicture}

\end{document}

An other solution by modifying the pic code so that the origin of the pic corresponds to the lowest vertex:

\documentclass{article}

\usepackage[papersize={5.5in,8.5in},margin=0.6in]{geometry}
\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\tikzset{%
    dartstyle/.style={kite,draw,kite vertex angles=60,inner sep=0.125in,outer sep=0pt,fill=#1},
    pics/quiltdart/.style={%
        code={%
          \node[dartstyle=red,anchor=lower vertex](base) {};
          \node[dartstyle=white,anchor=left vertex] at (base.upper vertex) {};
          \node[dartstyle=white,anchor=right vertex] at (base.upper vertex) {};
          \node[dartstyle=red,anchor=lower vertex] at (base.upper vertex){};
        }%
    }%
}

\parindent0pt

\begin{document}

%This was easy:

%\tikz \pic {quiltdart};

%\bigskip

%This, not so much\dots


\begin{tikzpicture}

% first copy
\foreach \i in {0,60,...,300}{
\pic[rotate =\i,transform shape] {quiltdart};
}
% second copy
\foreach \i in {0,60,...,300}{
\pic[rotate =\i,transform shape] at(0,8){quiltdart};
}
\end{tikzpicture}
\end{document}

Answer 2

With just a path, without pics or nodes

\documentclass{article}

\usepackage[papersize={5.5in,8.5in},margin=0.6in]{geometry}
\usepackage{tikz}

\newcommand{\mydart}[1][]{
    \filldraw[black, fill=red, even odd rule,#1] (0,0)--++(60:1)--++(120:1)--++(240:1)--cycle (60:.5)--++(60:.5)--++(120:.5)--++(240:1)--++(120:.5)--++(60:.5)--cycle
}

\begin{document}

This was easy:

\tikz \mydart;

\bigskip

What about this ???

\begin{tikzpicture}
 \foreach \i in {0,60,...,300}{
  \mydart[rotate around={\i:(0,0)}];
  }

\end{tikzpicture}


or this ???

\begin{tikzpicture}
 \foreach \i in {0,60,...,300}{
  \mydart[shift={(\i:1)}, rotate=\i];
  }

\end{tikzpicture}

\end{document}

Answer 3

This is another approach, changing the pic. In my pic I draw four squares, but I changed the axes to 'deform' them.

Like this:

\documentclass[border=2mm,tikz]{standalone}

\definecolor{color0}{HTML}{FFFFFF} % white
\definecolor{color1}{HTML}{FF0000} % red

\tikzset
{%
  pics/quiltdart/.style={
    code={%
      \pgfmathsetmacro\y{sin(60)}
      \begin{scope}[x={(0.5 cm,\y cm)}, y={(-0.5 cm,\y cm)}]
        \foreach\i in {0,1} \foreach\j in {0,1}
        {
          \pgfmathtruncatemacro\c{Mod(\i+\j+1,2)}
          \draw[fill=color\c] (\i,\j) -- (\i,\j+1) -- (\i+1,\j+1) -- (\i+1,\j) -- cycle;
        } 
      \end{scope}
    }},
}

\begin{document}
\begin{tikzpicture}[line join=round]
\foreach\a in {0,60,...,300}
  \pic[rotate=\a] {quiltdart};
\end{tikzpicture}
\end{document}

Answer 4

Compile with Asymptote or at http://asymptote.ualberta.ca/

size(5cm);

picture pic;
unitsize(pic,1cm);

path g=(0,0)--0.5*dir(60)--0.5*dir(0)--0.5*dir(-60)--cycle;
draw(pic,g^^shift(0.5*dir(0))*g);
filldraw(pic,shift(0.5*dir(60))*g^^shift(0.5*dir(-60))*g,red,black);

for (int i=0;i<6;++i)
  add(rotate(i*60,dir(-60))*pic);

If you can any issues with my code, please comment.

Answer 5

New solution

\documentclass[border=5mm]{standalone}
\usepackage[rgb]{xcolor}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\tikzset{quiltdart/.pic={%
\def\n{#1} % the number of quiltdart
% random colors from OP
\pgfmathsetmacro{\myhuei}{rnd}
\pgfmathsetmacro{\myhueii}{rnd}
\pgfmathsetmacro{\myhueiii}{rnd}
\definecolor{mycolori}{hsb}{\myhuei,1,1}
\definecolor{mycolorii}{hsb}{\myhueii,0.25,1}
\definecolor{mycoloriii}{hsb}{\myhueiii,1,1}
        
\def\basicdart{(0,0)--(90-360/\n:1)--+(0,1)--(0,1)--cycle}          
\foreach \i in {0,...,\n}{
\draw[fill=mycoloriii,rotate=\i*360/\n,shift={(90-360/\n:1)},shift={(0,1)}] \basicdart;
\draw[fill=mycolori,rotate=\i*360/\n] \basicdart;
\draw[fill=mycolorii,rotate=\i*360/\n,shift={(0,1)}] \basicdart;
\draw[fill=mycolorii,rotate=\i*360/\n,shift={(0,1)},xscale=-1] \basicdart;
}
}}

\newcounter{myquilt}
\setcounter{myquilt}{2} 
\foreach \j in {1,...,5}
\foreach \i in {1,...,8}
{\stepcounter{myquilt}
\path (6*\i,-6*\j) pic[scale=.6]{quiltdart=\themyquilt} 
% +(-90:2.6) node{$n=$ \themyquilt}   % show the number of quiltdart
;
}
\end{tikzpicture}
\end{document} 

Old solutions I guess the essential issue is centering/not centering pic, neither pic of nodes nor rotate. This turns to quite interesting situations:

• pic is/is not centered at the origin (name dart)
• pic of pics (name quiltdart).

I add the default values for parameters of the pics. The option [rotate,shift] is used instead of [rotate around]. I hope the code and the pictures are self-exlpained.

\documentclass[border=5mm,tikz]{standalone}
% Multi-parameters pic with default
\tikzset{
pics/dart/.style args={#1 and #2}{code={%
\draw[fill=#1] (-120:1)--(60:1)--([turn]60:1)--(120:1)--(-60:1)--([turn]-60:1)--cycle;
\draw[fill=#2] (-120:1)--(60:1)--(0:1)--(-60:1)--(120:1)--(180:1)--cycle;
}},
pics/dart/.default={red and white}
}

% Multi-parameters pic of pics with default
\tikzset{pics/quiltdart/.style args={#1 and #2}{code={%
\foreach \i in {0,...,5}
\path (0,0) pic[rotate=60*\i,shift={(0,-sqrt(3))}]{dart={#1 and #2}};
}},
pics/quiltdart/.default={red and white}
}

\begin{document}
\begin{tikzpicture}
\path 
(0,0) pic{dart} node[above=2.5cm,scale=2]{\verb|\pic{dart}|}
(18,0) pic{dart={magenta and cyan}} node[above=2.5cm,scale=2]{\verb|\pic{dart={magenta and cyan}}|};

\foreach \i in {0,...,5}
\path (0,-10) pic[rotate=60*\i,shift={(0,-sqrt(3))}]{dart};
\path (0,-10) node[above=3.5cm,scale=2,align=center]{Good\\
    \verb|\foreach \i in {0,...,5}|\\
    \verb|\pic[rotate=60*\i,shift={(0,-sqrt(3))}]{dart}|};
\path 
(18,-10) pic{quiltdart={magenta and cyan}} node[above=3.5cm,scale=2,align=center]{Better\\
    \verb|\pic{quiltdart={magenta and cyan}}|};
\end{tikzpicture}
\end{document} 
 

Some examples of quilt decorations

1. A tiling of the plane

\begin{tikzpicture}
\foreach \i in {0,...,5}
\foreach \j in {0,...,4}
\path (5*\i,-5*\j) pic{quiltdart};
\end{tikzpicture}

2. A green quilt

\begin{tikzpicture}
\foreach \i in {0,...,5}
\foreach \j in {0,...,4}
\path (8*\i,-8*\j) pic{quiltdart={green and white}};
\end{tikzpicture}

Update Asymptote version pic of pics can be translated from TikZ to Asymptote.

unitsize(1cm);

// creating dart
picture dart;
unitsize(dart,1cm);
path p=dir(-120)--dir(60)--dir(0)--dir(-60)--dir(120)--dir(180)--cycle;
path q=dir(-120)--dir(60)--sqrt(3)*dir(90)--dir(120)--dir(-60)--sqrt(3)*dir(-90)--cycle;
filldraw(dart,p,pink,black);
filldraw(dart,q,purple,black);

// creating quiltdart from darts
picture quiltdart;
unitsize(quiltdart,1cm);
for(int i=0;i<6;++i)
add(quiltdart,rotate(i*60)*shift(0,-sqrt(3))*dart);

// Here is the quilt
for (int i=0;i<6;++i)
for (int j=0;j<3;++j)
add(shift(8*i,-8*j)*quiltdart);

shipout(bbox(1cm,invisible));

Update 2: General case A generalization of n-point-star quiltdarts. Sometimes, the general problem is easier to deal with a particular problem. It is how I feel for the situation of the new update answer of OP.

Idea is simple, straight forward of creating a function with parameter n. There 3 classes; each class is made from rotations of the basic dart; a small care for the middle class.

n=20 quiltdart(20,yellow,magenta,purple);

// http://asymptote.ualberta.ca/
unitsize(1cm);
// the basic dart
path dart(int n){
pair A=(0,0),D=(0,1),B=dir(90-360/n),C=B+D-A;
return A--B--C--D--cycle;
}

// the quiltdart of three classes
void quiltdart(int n, pen innerpen, pen middlepen, pen outerpen){
for(int i=0;i<n;++i){
transform rot=rotate(i*360/n);  
path outerclass=rot*shift((0,1)+dir(90-360/n))*dart(n);
path middleclass1=rot*shift(0,1)*dart(n);
path middleclass2=rot*shift(0,1)*xscale(-1)*dart(n);
path innerclass=rot*dart(n);
filldraw(outerclass,outerpen,black);
filldraw(middleclass1,middlepen,black);
filldraw(middleclass2,middlepen,black);
filldraw(innerclass,innerpen,black);
}} 

quiltdart(20,yellow,magenta,purple);
shipout(bbox(1cm,invisible));

n=4 quiltdart(4,yellow,orange,green);

n=50 quiltdart(50,yellow,green,red);

Update 3: A general solution with TikZ. n=45 is the maximal number that TikZ/TeX can compile without irritating and throwing up "Dimension too large" error.

\documentclass[border=5mm,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\def\n{45}
\def\basicdart{(0,0)--(90-360/\n:1)--+(0,1)--(0,1)--cycle}          
\foreach \i in {0,...,\n}{
\draw[fill=magenta,rotate=\i*360/\n,shift={(90-360/\n:1)},shift={(0,1)}] \basicdart;
\draw[fill=yellow,rotate=\i*360/\n] \basicdart;
\draw[fill=orange,rotate=\i*360/\n,shift={(0,1)}] \basicdart;
\draw[fill=orange,rotate=\i*360/\n,shift={(0,1)},xscale=-1] \basicdart;
}
\end{tikzpicture}
\end{document} 

Answer 6

A trivial solution with PSTricks.

\documentclass[pstricks]{standalone}

\newcommand\x[1][red]{%
    \pspolygon[fillcolor=#1]
        (0,0)(1,0)(!1 60 PtoC exch 1 add exch)(1;60)}
        
\def\y{%
    \x\rput(1,0){\x[white]}
    \rput(1;60){\x[white]\rput(1,0){\x}}}
    
\begin{document}
\begin{pspicture}[fillstyle=solid](-4,-4)(4,4)
    \foreach \i in {0,60,...,300}{\rput{\i}(0,0){\y}}
\end{pspicture}
\end{document}