Ngtjyty

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.

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}

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}