TikZ: Draw the smallest rectangle containing given points with sides parallel to coordinate axes

Question

I need a TikZ macro to draw the smallest rectangle around a list of points, with sides parallel to the coordinate axes. In a perfect world it would work with any number of points greater than 1, but I would be happy if it just worked with 3. The points will usually be of the form

([yshift=10pt] A.north)

That is, they will generally be anchors of shapes, possibly shifted manually.

Answer 1

Code

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,fit,positioning}

\begin{document}

\begin{tikzpicture}
    % some nodes
    \node[fill=red,circle,inner sep=2mm] (A) at (0,0) {};
    \node[fill=blue,circle,inner sep=4mm] (B) at (4,-1) {};
    \node[fill=violet,circle,inner sep=3mm] (C) at (1,3) {};

    % a node, relatively shifted
    \node[fill=orange,circle] (D) at ([yshift=5mm,xshift=15mm] A.north) {};

    % outer fit
    \node[thick,draw=red,fit=(A)(B)(C)] {};
    \node[thick,draw=blue,fit=(A)(B)(C),inner sep=0] {};

    % inner fit
    \node[thick,draw=red,fit=(A.east)(B.north west)(C.south),densely dotted] {};
    \node[thick,draw=blue,fit=(A.east)(B.north west)(C.south),inner sep=0,densely dotted] {};
    \node[thick,draw=violet,fit=(A.east)(B.north west)(C.south),inner sep=-3pt,densely dotted] {};

    % center fit with shifted node, as ([options] node) does not work
    \node[thick,draw=orange,fit=(A.center)(B.center)(D.center),densely dashed,inner sep=0] {};

    % same as above with calc's ($()+()$); note that you can't use coordinates as (x,y), you have
    %   to enclose the coordinates in braces: ({x,y})
    \node[thick,draw=orange,fit=(A.center)(B.center)($(A.north)+({1.5,0.5})$),densely dashed] {};
\end{tikzpicture}

\end{document}

Output