Zooming without magnifying line widths and points

Question

I tried the approach described in https://tex.stackexchange.com/a/129307/21557 to magnify a part of an image without magnifying line widths. I also don't want the point to be magnified. In my example however the point is also magnified (see below). How can I avoid this?

I also want to draw additional stuff inside he magnified part, im my example above an angle. How can I interpret the units for that part?

\documentclass[tikz,border=5mm]{standalone}


\usetikzlibrary{calc,decorations.markings}

\tikzset{
tangent/.style={
        decoration={
            markings,% switch on markings
            mark=
                at position #1
                with
                {
                    \coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
                    \coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
                    \coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
                }
        },
        postaction=decorate
    },
    use tangent/.style={
        shift=(tangent point-#1),
        x=(tangent unit vector-#1),
        y=(tangent orthogonal unit vector-#1)
    },
    use tangent/.default=1
  }

\usetikzlibrary{calc,positioning,angles}

\begin{document}
\begin{tikzpicture}[
    % Style for the spy nodes and the connection line
    spy/.style={%
        draw,orange,
        line width=1pt,
        circle,inner sep=0pt,
    },
]
    % Parameters

    %% size of the spy-in nodes
    \def\spyviewersize{4.25cm}

    %% (line width of the spy nodes) / 2
    %% we need this for clipping later
    \def\spyonclipreduce{0.5pt}

    %% first zoom
    %%% factor
    \def\spyfactorI{20}
    %%% spy in point
    \coordinate (spy-in 1) at (8,0);
    %%% spy on point
    \coordinate (spy-on 1) at (20:3);% sould be on the curve



    %% the graph/picture
    \def\pik{
      \pgfmathsetmacro{\al}{20}
      \draw[tangent={\al/360}] (0,0) circle (3);
      \draw[use tangent,green] (-2,0) -- (2,0) coordinate (XA);
      \draw[use tangent,red] (-2,0.3) -- (2,-0.3) coordinate (XB);
      \fill (\al:3) circle (0.05) coordinate (P) node[right]{$P$};
    }


    % draw the original picture
    \pik

    % first zoom
    %% spy on node
    \node[spy,minimum size={\spyviewersize/\spyfactorI}] (spy-on node 1) at (spy-on 1) {};
    %% spy in node
    \node[spy,minimum size=\spyviewersize] (spy-in node 1) at (spy-in 1) {};
    \begin{scope}
        \clip (spy-in 1) circle (0.5*\spyviewersize-\spyonclipreduce);
        \pgfmathsetmacro\sI{1/\spyfactorI}
        \begin{scope}[
            shift={($\sI*(spy-in 1)-\sI*(spy-on 1)$)},
            scale around={\spyfactorI:(spy-on 1)},
        ]
        \pik
        %%
        \pic [pic text=$\varphi$,draw,angle radius=50,blue,fill,fill
        opacity=0.5]{angle=XB--P--XA};
        %% How to interpret the measure 50 for the angle radius
        \end{scope}
    \end{scope}
    %% connect the nodes
    \draw [spy] (spy-on node 1) -- (spy-in node 1);
\end{tikzpicture}
\end{document}

Answer 1

You should use a node with a circled shape instead of a “real” circle, as the node won’t be scaled:

\documentclass[tikz,border=5mm]{standalone}

\usetikzlibrary{calc,decorations.markings,positioning,angles}

\tikzset{
tangent/.style={
        decoration={
            markings,% switch on markings
            mark=
                at position #1
                with
                {
                    \coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
                    \coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
                    \coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
                }
        },
        postaction=decorate
    },
    use tangent/.style={
        shift=(tangent point-#1),
        x=(tangent unit vector-#1),
        y=(tangent orthogonal unit vector-#1)
    },
    use tangent/.default=1
  }

\begin{document}
\begin{tikzpicture}[
    % Style for the spy nodes and the connection line
    spy/.style={%
        draw,orange,
        line width=1pt,
        circle,inner sep=0pt,
    },
]
    % Parameters

    %% size of the spy-in nodes
    \def\spyviewersize{4.25cm}

    %% (line width of the spy nodes) / 2
    %% we need this for clipping later
    \def\spyonclipreduce{0.5pt}

    %% first zoom
    %%% factor
    \def\spyfactorI{20}
    %%% spy in point
    \coordinate (spy-in 1) at (8,0);
    %%% spy on point
    \coordinate (spy-on 1) at (20:3);% sould be on the curve

    %% the graph/picture
    \def\pik{
      \pgfmathsetmacro{\al}{20}
      \draw[tangent={\al/360}] (0,0) circle (3);
      \draw[use tangent,green] (-2,0) -- (2,0) coordinate (XA);
      \draw[use tangent,red] (-2,0.3) -- (2,-0.3) coordinate (XB);
      \node[fill,circle,inner sep=1pt,label={0:$P$}] (P) at (\al:3) {}; % <- change real circle to node
    }

    % draw the original picture
    \pik

    % first zoom
    %% spy on node
    \node[spy,minimum size={\spyviewersize/\spyfactorI}] (spy-on node 1) at (spy-on 1) {};
    %% spy in node
    \node[spy,minimum size=\spyviewersize] (spy-in node 1) at (spy-in 1) {};
    \begin{scope}
        \clip (spy-in 1) circle (0.5*\spyviewersize-\spyonclipreduce);
        \pgfmathsetmacro\sI{1/\spyfactorI}
        \begin{scope}[
            shift={($\sI*(spy-in 1)-\sI*(spy-on 1)$)},
            scale around={\spyfactorI:(spy-on 1)},
        ]
        \pik
        %%
        \pic[draw,angle radius=50,fill=blue!50,pic text=$\varphi$]{angle=XB--P--XA};
        %% How to interpret the measure 50 for the angle radius
        \end{scope}
    \end{scope}
    %% connect the nodes
    \draw [spy] (spy-on node 1) -- (spy-in node 1);
\end{tikzpicture}
\end{document}

Result:

Edit: Amended the code for the coloring and label of the angle in order to make the label opaque.