Cfxtrjtrk

This question is a kind of continuation this answer. There, it remains unclear which is the origin of the white space around the node content, if a square shape is used, and I would like to understand this. Given the following MWE

documentclass[tikz, border=1mm]{standalone}

usetikzlibrary{shapes.geometric}



begin{document}

    begin{tikzpicture}[every node/.style={draw, inner sep=0}]

        node[regular polygon,regular polygon sides=4] (a) {XX};

        node[regular polygon,regular polygon sides=100, blue] (b) {XX};

        node[circle] (c) {XX};

        foreach a in {north,south,east,west,north east,south east,north west,south west}{

            fill[red] (a.a) circle(0.5pt);

            fill[yellow] (b.a) circle(0.25pt);

            fill[orange] (c.a) circle(0.25pt);

        }

    end{tikzpicture}

end{document}

I am a bit surprised that the black circle has a radius which is smaller than that of the inscribed circle in the polygon, since the pgf manual says

[...] the border of the polygon is always constructed using the
incircle, whose radius is calculated to tightly fit the node contents
(including any inner sep).

To show what I would have expected and what I would like to have I added a blue "fake circle" to the MWE as a regular polygon with 100 sides. Is there a way to draw such a blue circle using the circle shape, i.e. node[circle, ...]{XX};? Playing by hand with inner sep is not an option for me.

As clarification/additional information, I am interested in having a node shape to be used in a wider context, i.e. not in relation with the square. And also receiving an explanation about why the 4-sides polygon leaves so much space despite the inner sep=0 would be highly appreciated.

UPDATE: From the comments, indeed, there is some room of interpretation in the question. In short, I would like to answer these questions.

1. How is it possible to have a Circle shape (or Circle tikzstyle) that draws exactly the inscribed circle of the correspondent regular polygon around a given node content?


2. Where does the discrepancy between black circle and square in my MWE come from?


3. If easier (I can also use this other approach), how is it possible to have a Regular Polygon shape (or tikzstyle) that has as inscribed circle the correspondent circle around a given node content?

The "inner circle" in shapes.geometric has a radius that is half of the longest side of the content box plus the inner sep, and multiplied by 1.4142136, which is approximately sqrt(2). So to obtain a circle shape that has this behavior you can define a new shape, let's say Circle (with capital C) that is a slight modification of the existing ellipse shape.

documentclass[tikz, border=7pt, convert={density=4200}]{standalone}

usetikzlibrary{shapes.geometric}

makeatletter

pgfdeclareshape{Circle}

%

% Draws a circle around the text

% (based on the original ellipse shape)

%

{%

  savedanchorcenterpoint{%

    pgf@x=.5wdpgfnodeparttextbox%

    pgf@y=.5htpgfnodeparttextbox%

    advancepgf@y by-.5dppgfnodeparttextbox%

  }%

  savedanchorradius{%

    %

    % Calculate ``height radius''

    %

    pgf@y=.5htpgfnodeparttextbox%

    advancepgf@y by.5dppgfnodeparttextbox%

    pgfmathsetlengthpgf@yb{pgfkeysvalueof{/pgf/inner ysep}}%

    advancepgf@y bypgf@yb%

    %

    % Calculate ``width radius''

    %

    pgf@x=.5wdpgfnodeparttextbox%

    pgfmathsetlengthpgf@xb{pgfkeysvalueof{/pgf/inner xsep}}%

    advancepgf@x bypgf@xb%

    %

    % Adjust

    %

    % ==============================

    % added to ellipse shape to become circle

    ifdimpgf@y>pgf@x%

            pgf@xpgf@y%

    else%

        pgf@ypgf@x%

    fi%

    % ==============================

    pgf@x=1.4142136pgf@x%

    pgf@y=1.4142136pgf@y%

    %

    % Adjust height, if necessary

    %

    pgfmathsetlengthpgf@yc{pgfkeysvalueof{/pgf/minimum height}}%

    ifdimpgf@y<.5pgf@yc%

      pgf@y=.5pgf@yc%

    fi%

    %

    % Adjust width, if necessary

    %

    pgfmathsetlengthpgf@xc{pgfkeysvalueof{/pgf/minimum width}}%

    ifdimpgf@x<.5pgf@xc%

      pgf@x=.5pgf@xc%

    fi%

    %

    % Add outer sep

    %

    pgfmathsetlength{pgf@xb}{pgfkeysvalueof{/pgf/outer xsep}}%

    pgfmathsetlength{pgf@yb}{pgfkeysvalueof{/pgf/outer ysep}}%

    advancepgf@x bypgf@xb%

    advancepgf@y bypgf@yb%

  }%



  %

  % Anchors

  %

  anchor{center}{centerpoint}%

  anchor{mid}{centerpointpgfmathsetlengthpgf@y{.5ex}}%

  anchor{base}{centerpointpgf@y=0pt}%

  anchor{north}

  {

    pgf@process{radius}

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@y bypgf@ya

  }%

  anchor{south}

  {

    pgf@process{radius}

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@y by-pgf@ya

  }%

  anchor{west}

  {

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x by-pgf@xa

  }%

  anchor{mid west}

  {%

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x by-pgf@xa%

    pgfmathsetlengthpgf@y{.5ex}

  }%

  anchor{base west}

  {%

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x by-pgf@xa%

    pgf@y=0pt

  }%

  anchor{north west}

  {

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@x by-0.707107pgf@xa

    advancepgf@y by0.707107pgf@ya

  }%

  anchor{south west}

  {

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@x by-0.707107pgf@xa

    advancepgf@y by-0.707107pgf@ya

  }%

  anchor{east}

  {%

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x bypgf@xa

  }%

  anchor{mid east}

  {%

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x bypgf@xa%

    pgfmathsetlengthpgf@y{.5ex}

  }%

  anchor{base east}

  {%

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@process{centerpoint}

    advancepgf@x bypgf@xa%

    pgf@y=0pt

  }%

  anchor{north east}

  {

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@x by0.707107pgf@xa

    advancepgf@y by0.707107pgf@ya

  }%

  anchor{south east}

  {

    pgf@process{radius}

    pgf@xa=pgf@x%

    pgf@ya=pgf@y%

    pgf@process{centerpoint}

    advancepgf@x by0.707107pgf@xa

    advancepgf@y by-0.707107pgf@ya

  }%

  anchorborder{

    edefpgf@marshal{%

      noexpandpgfpointborderellipse

      {noexpandpgfqpoint{thepgf@x}{thepgf@y}}

      {noexpandradius}%

    }%

    pgf@marshal%

    pgf@xa=pgf@x%

    pgf@ya=pgf@y%

    centerpoint%

    advancepgf@x bypgf@xa%

    advancepgf@y bypgf@ya%

  }%



  %

  % Background path

  %

  backgroundpath

  {

    pgf@process{radius}%

    pgfutil@tempdima=pgf@x%

    pgfutil@tempdimb=pgf@y%

    pgfmathsetlength{pgf@xb}{pgfkeysvalueof{/pgf/outer xsep}}%

    pgfmathsetlength{pgf@yb}{pgfkeysvalueof{/pgf/outer ysep}}%

    advancepgfutil@tempdima by-pgf@xb%

    advancepgfutil@tempdimb by-pgf@yb%

    pgfpathellipse{centerpoint}{pgfqpoint{pgfutil@tempdima}{0pt}}{pgfqpoint{0pt}{pgfutil@tempdimb}}%

  }%

}%

makeatother



begin{document}

    begin{tikzpicture}[nodes={draw, inner sep=0}]

        node[regular polygon,regular polygon sides=4] (a) {XX};

        node[Circle, blue] (b) {XX};

        node[circle] (c) {XX};

        foreach a in {north,south,east,west,north east,south east,north west,south west}{

            fill[red] (a.a) circle(0.5pt);

            fill[yellow] (b.a) circle(0.25pt);

            fill[orange] (c.a) circle(0.25pt);

        }

    end{tikzpicture}

end{document}

Addendum:

If you want to go the other way and create a circumscribed polygon around the standard circle node style, that do not use low level tricks, you can define circumscribed polygon that use append after command to add well sized regular polygon. This is not a robust code for meany reasons, it is just a proof of concept :

documentclass[tikz,border=7pt,convert={density=4200}]{standalone}

usetikzlibrary{calc,shapes.geometric}



% don't tell me to not use tikzstyle ;)

tikzstyle{circumscribed polygon}[draw]=[

  circle,draw=none,fill=none,shade=none,

  append after command={

    let p1=($(tikzlastnode.west)-(tikzlastnode.east)$),

        n1 = {(veclen(p1)-pgflinewidth)/2.828427} % 2*sqrt(2) = 2.8284271247461903

    in

    (tikzlastnode.center) node[regular polygon,  inner sep=n1, #1]{}

  }

]

begin{document}

  begin{tikzpicture}[inner sep=1mm]

    foreach~in {3,...,7}

      node[circumscribed polygon={draw=blue!~0!green,regular polygon sides=~}] {XX};

    node[circle,draw=red] {XX};

  end{tikzpicture}

end{document}

Using through library of Tikz.

documentclass[tikz, border=1mm]{standalone}

usetikzlibrary{shapes.geometric,through}



begin{document}

    begin{tikzpicture}[every node/.style={draw, inner sep=0}]

        node[regular polygon,regular polygon sides=4] (a) {XX};

        node (b) [draw,blue, circle through=(a.north)] at (a.center) {XX};

        node[circle] (c) {XX};

         foreach a in {north,south,east,west,north east,south east,north west,south west}{

            fill[red] (a.a) circle(0.5pt);

            fill[yellow] (b.a) circle(0.25pt);

            fill[orange] (c.a) circle(0.25pt);

        }



    end{tikzpicture}

end{document}

Just to share a different way to achieve what Kpym did in his very nice answer declaring a new shape, I thought one could have simply a Circle style which sets properly the minimum size of a circle shape (in this particular case it is always true that the content will never exceed the minimum size since we are trying to enlarge the circle). It should work for any node content, no matter if its width is larger than its height or vice-versa. A couple of remarks:

• In this approach the node name and the node position must be declared before the options or inside them using the name and at keys, respectively.


• A Circle inner sep has to be specified before the Circle style, but it might easily be improved, if needed otherwise.

Here the code:

documentclass[tikz, border=1mm]{standalone}

usetikzlibrary{shapes.geometric}



tikzset{%

    Square/.style={regular polygon, regular polygon sides=4},

    Circle/.style={%

        circle,

        /utils/exec={%

            pgfmathsetmacropolygonIncircleDiameter{

                sqrt(2)*max(width("#1")+2*pgfshapeinnerxsep, height("#1") + depth("#1") + 2 * pgfshapeinnerysep)

            }

        },

        minimum size=polygonIncircleDiameter,

        node contents={#1}

    }

}



begin{document}

    begin{tikzpicture}

        node[inner sep=0, Square, draw=cyan] at (0,0) {xx};

        node[inner sep=0, Circle={xx}, draw=blue];

        node[Square, draw=cyan] at (1,0) {i};

        node[Circle={i}, draw=blue, at={(1,0)}];

    end{tikzpicture}

end{document}