Rounded polygons

Question

I would like to realize beautiful rounded polygons enclosing some nodes.

If we use \draw[rounded corners] the resulting polygon does not include our vertices.

\documentclass[border=5]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}

%Coordinates of the vertices
\foreach \i/\r in {0/1,1/0.8,2/1.2,3/1,4/0.9,5/1.1}
    \coordinate (c\i) at (60*\i:\r) {};

%The vertices
\foreach \i in {0,...,5} \node[fill=black,circle,inner sep=1pt] at (c\i) {};

%The Polygon
\draw[rounded corners=5] (c0)--(c1)--(c2)--(c3)--(c4)--(c5)--cycle;

\end{tikzpicture}
\end{document}

We can shift the center points of the polygon like this, but for each node the direction of shifting changes and had to be calculated.

I know of the two approaches in this very much related Question but both answers have their drawbacks. Symbol 1s answer actually uses filldraw so we can not have multiple polygons intersect. My answer is just ridiculously slow for compiling.

So my answer is: What is a nice way of drawing a polygon around some nodes?

Answer 1

I do not think it is necessary to reinvent this since this has already a very nice answer here.

\documentclass[tikz]{standalone}
\makeatletter
\usetikzlibrary{decorations,backgrounds}
\def\pgfdecoratedcontourdistance{0pt}
\pgfset{
  decoration/contour distance/.code=%
    \pgfmathsetlengthmacro\pgfdecoratedcontourdistance{#1}}
\pgfdeclaredecoration{contour lineto closed}{start}{%
  \state{start}[
    next state=draw,
    width=0pt,
    persistent precomputation=\let\pgf@decorate@firstsegmentangle\pgfdecoratedangle]{%
    \pgfpathmoveto{\pgfpointlineattime{.5}
      {\pgfqpoint{0pt}{\pgfdecoratedcontourdistance}}
      {\pgfqpoint{\pgfdecoratedinputsegmentlength}{\pgfdecoratedcontourdistance}}}%
  }%
  \state{draw}[next state=draw, width=\pgfdecoratedinputsegmentlength]{%
    \ifpgf@decorate@is@closepath@%
      \pgfmathsetmacro\pgfdecoratedangletonextinputsegment{%
        -\pgfdecoratedangle+\pgf@decorate@firstsegmentangle}%
    \fi
    \pgfmathsetlengthmacro\pgf@decoration@contour@shorten{%
      -\pgfdecoratedcontourdistance*cot(-\pgfdecoratedangletonextinputsegment/2+90)}%
    \pgfpathlineto
      {\pgfpoint{\pgfdecoratedinputsegmentlength+\pgf@decoration@contour@shorten}
      {\pgfdecoratedcontourdistance}}%
    \ifpgf@decorate@is@closepath@%
      \pgfpathclose
    \fi
  }%
  \state{final}{}%
}
\makeatother
\tikzset{
  contour/.style={
    decoration={
      name=contour lineto closed,
      contour distance=#1
    },
    decorate}}
\begin{document}
\begin{tikzpicture}
\foreach \i/\r in {0/1,1/0.8,2/1.2,3/1,4/0.9,5/1.1}
    \coordinate (c\i) at (60*\i:\r);
\foreach \i in {0,...,5} \node[fill=black,circle,inner sep=1pt] at (c\i) {};

\draw[preaction={contour=-5pt,rounded corners=5,draw}] (c0)--(c1)--(c2)--(c3)--(c4)--(c5)--cycle;   
\end{tikzpicture}
\end{document}

\draw[draw=none,preaction={contour=-5pt,rounded corners=5,draw}] (c0)--(c1)--(c2)--(c3)--(c4)--(c5)--cycle; 

Answer 2

You can calculate the barycenter of all vertices (in the code is the node (b)), and then scale the polygon relatively to its barycenter (in the code using scale around={1.3:(b)} stored in a style s).

\documentclass[tikz,border=7pt]{standalone}
\usetikzlibrary{calc}
\begin{document}
  \begin{tikzpicture}
    %Coordinates of the vertices
    \coordinate(b); % <-- will contain the barycenter of the vertices
    \foreach[count=\n from 0] \i/\r in {0/1,1/0.8,2/1.2,3/1,4/0.9,5/1.1}
        \path (60*\i:\r) coordinate (c\i) ($(c\i)!\n/(\n+1)!(b)$) coordinate(b);

    %The vertices
    \foreach \i in {0,...,5} \node[fill=black,circle,inner sep=1pt] at (c\i) {};

    %The rounded polygon
    \draw[rounded corners=5,s/.style={scale around={1.3:(b)}}]
      ([s]c0) foreach \i in{1,...,5}{--([s]c\i)}--cycle;

  \end{tikzpicture}
\end{document}