tikz: Getting angles in mindmaps right

Question

I'm starting to believe that tikz just wasn't meant for me...

how was I able to get this wrong:

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,calc,trees,mindmap,backgrounds,shadows}

\begin{document}

\begin{tikzpicture}
\path[mindmap,concept,concept color=red] (0,0) node (languages) {Languages} [clockwise from=90]
    child { node {Markdown} }
    child[ sibling angle=110, level distance=8cm] { node {R}  [clockwise from=130]
        child[ level distance = 4cm] { node {control structures (if, for, \mbox{while, repeat,} \mbox{next, break)}} }
        child[ sibling angle = 90, level distance=6cm] { node {data types} [clockwise from=110] 
            child { node {vectors} }
            child { node {lists} }
            child { node {matrices} }
            child { node {data frames} }
            child { node {factors} }
            child { node {dates} }
            child { node {time} }
            child { node {data.table} }
            child { node {missing values} }
        }
        child[ sibling angle = 20] { node {functions} }
    }
    child[sibling angle=130] { node {RMarkdown} }
;
\end{tikzpicture}

\end{document}

How come "functions" is not 20 degrees from "data types"? How does sibling angle work? (reading the manual was not helping)

What does not work

Does not work 1

Mark Wibrow's answer is great... or would be if working for me. Before getting into details of his functions, I should share an even more basic example that does not work for me:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{trees,mindmap}

\begin{document}
\begin{tikzpicture}[mindmap, concept color=blue!20, every child node/.style={concept}]

\node[concept] (languages) {O} [clockwise from=90, sibling angle=90]
  child { node {A} }
  child { node {B} }
  child { node {C}
   child { node {C1} }
   child { node {C1} }
   child { node {C1} }
  }
  child { node {D} };

\end{tikzpicture}
\end{document}

Does not work 2 - Strange result changes

Having small mindmap instead of mindmap looks suspiciously like Mark Wibrow's result (though this may be by chance):

Does not work 3 - Mark Wibrow's code

Using Mark Wibrow's last code brings the results shown by him, but if I change his [clockwise from=0, sibling angle=45] to [clockwise from=0, sibling angle=10] the result does not change for the C1-nodes.

What would be best

After playing around a lot I think what would be best, would be something like Mark Wibrow's angle list, but with not with absolute values, but that the list contains the angles from each node to the previous node. For example instead of (for seven nodes) [grow cyclic list={120,70,40,5,-30,-80,-100}] to have [grow cyclic list={120,-50,-30,-35,-35,-50,-20}].

Answer 1

It isn't amazingly clear from the manual (if at all), but when using the clockwise from key the angle B for the child node is basically:

B = A - (n-1)*s

where A is the start angle, n is the number of the current child, and s is the current value of the sibling angle (which could be set globally, locally or in a level, or every child style). So if the start angle is A=130 and the sibling angle is set to s=20 in the child options for the third child (n=3) then the angle for the node is B=130-(3-1)*20=90, which I think is what you get.

Therefore, if you use the clockwise from key and you want the nth child node to appear at a specific angle B then the sibling angle s should be set to:

s = (A - B) / (n-1)

Confusing? Well, maybe. But what might be of more use in this case is a grow cyclic absolute key in which the sibling angle given in the child options gives the absolute angle of the child. The sibling angle must be given for every child node (otherwise it will be whatever the sibling angle is set at in the current scope), but other growth functions can still be installed for (great, ...) grand children.

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{trees,mindmap}
\tikzset{grow cyclic absolute/.style={%
  growth function=\tikzgrowcyclicabsolute}}
\def\tikzgrowcyclicabsolute{%
  \pgftransformshift{%
   \pgfpointpolar{\pgfkeysvalueof{/tikz/sibling angle}}%
    {\the\tikzleveldistance}}}
\begin{document}
\begin{tikzpicture}[small mindmap, concept color=blue!20,  
  every child node/.style={concept}]
\node [concept] (languages) 
  {O} [grow cyclic absolute] 
    child [sibling angle=90]  { node {A} }
    child [sibling angle=0]   { node {B} }
    child [sibling angle=-45] { node {C} 
      [clockwise from=0, sibling angle=45]
      child { node {C1} }
      child { node {C1} }
      child { node {C1} }
    }
    child [sibling angle=210] { node {D} };
\end{tikzpicture}
\end{document}

To avoid the annoyance of cluttering up the child code with endless sibling angles, an alternative grow cyclic list growth function could be used to specify the growth angles when the growth function set:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{trees,mindmap}
\tikzset{grow cyclic list/.code={%
  \def\tikzgrowthpositions{{#1}}%
  \foreach \n [count=\i,remember=\i]in {#1}{}%
  \let\tikzgrowthpositionscount=\i%
  \tikzset{growth function=\tikzgrowcycliclist}}}
\def\tikzgrowcycliclist{%
  \pgftransformshift{%
    \pgfpointpolar{\tikzgrowthpositions[mod(\the\tikznumberofcurrentchild-1,\tikzgrowthpositionscount)]}%
      {\the\tikzleveldistance}}}
\begin{document}
\begin{tikzpicture}[small mindmap, concept color=blue!20,  
  every child node/.style={concept}]
\node [concept] (languages) 
  {O} [grow cyclic list={90,0,-45,210}] 
    child { node {A} }
    child { node {B} }
    child { node {C} 
      [clockwise from=0, sibling angle=45]
      child { node {C1} }
      child { node {C1} }
      child { node {C1} }
    }
    child { node {D} };
\end{tikzpicture}
\end{document}

The result is the same as before.

The advantage of being specifying the angle absolutely, is that any angles can be pre-processed into absolute angles. The following demonstrates an example of this, where given a starting angle, the angles between siblings can be specified in a list. This list is pre-processed into absolute angles.

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{trees,mindmap}
\makeatletter
\tikzset{%
grow clockwise/.code args={first at #1 then turning #2}{%
  \pgfmathparse{#1}%
  \let\tikzgrowthpositions=\pgfmathresult%
  \let\tikz@tmpangle=\pgfmathresult%
  \c@pgf@counta=1\relax%
  \pgfutil@for\tikz@tmp:=#2\do{%
    \advance\c@pgf@counta by1\relax%
    \pgfmathparse{Mod(\tikz@tmpangle-\tikz@tmp, 360)}%
    \let\tikz@tmpangle=\pgfmathresult%
    \edef\tikzgrowthpositions{\tikzgrowthpositions,\tikz@tmpangle}%
  }%
  \edef\tikzgrowthpositions{{\tikzgrowthpositions}}%
  \edef\tikzgrowthpositionscount{\the\c@pgf@counta}%
  \tikzset{growth function=\tikzgrowcycliclist}%
}}
\def\tikzgrowcycliclist{%
  \pgftransformshift{%
    \pgfpointpolar{\tikzgrowthpositions[mod(\the\tikznumberofcurrentchild-1,\tikzgrowthpositionscount)]}%
      {\the\tikzleveldistance}}}
\begin{document}
\begin{tikzpicture}[small mindmap, concept color=blue!20,  
  every child node/.style={concept}]
\node [concept] (languages) 
  {O} [grow clockwise={first at 90 then turning 90,45,105}] 
    child { node {A} }
    child { node {B} }
    child { node {C} 
      [clockwise from=0,  level 2/.append style={sibling angle=60}]
      child { node {C1} }
      child { node {C1} }
      child { node {C1} }
    }
    child { node {D} };
\end{tikzpicture}
\end{document}

The result is the same as before.