Cómo deformar el contorno en tikz

Cómo deformar el contorno en tikz

Estoy tratando de descubrir cómo puedo conectar la curva de A a K con el punto superior derecho. En otras palabras, quiero que todavía quede un poco más del círculo en la parte derecha de la trama; En este momento tengo una línea recta a lo largo de K a H(...) pero preferiría una curva un poco más de K a H(...). ¿Cómo hago esto? Además, si quisiera otro pequeño semicírculo encima del punto, digamos x=-1,5, y=0,2, y también uno debajo de x=-1,5, y=0,2, ¿hay alguna manera de hacer esto sin arruinarlo? ¿imagen? ¡Gracias! Hasta ahora tengo algo que se parece a esto (no exactamente, pero parecido):

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.markings,positioning}
\begin{document}
        \begin{tikzpicture}
        %configurable parameters
        \def\gap{0.4}
        \def\bigradius{4}
        \def\littleradius{1}
        %axes
        \draw[line width=2pt,->](-1.5*\bigradius,0) -- (1.5*\bigradius,0)
        (0,-1.5*\bigradius) -- (0,1.5*\bigradius);
        \draw[line width=2pt,->] (0,0)--(45:\littleradius);
        \draw[line width=2pt,->](0,0) -- (135:\bigradius); \node[above
        right] at (45:\littleradius/1.5) {\large\bf{$\varepsilon$}};
        \draw[line width=1pt,decoration={markings,
            mark=at position 0.07 with{\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.17 with{\arrow[line width =2pt]{>}},
            mark=at position 0.27 with{\arrow[line width =2pt]{>}},
            mark=at position 0.35 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.47 with{\arrow[line width =2pt]{>}},
            mark=at position 0.53 with{\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.6 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.65 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.7 with{\arrow[line width =2pt]{>}},
            mark=at position 0.8 with{\arrow[line width =2pt]{>}},
            mark=at position 0.85 with{\arrow[line width =2pt]{>}},
            mark=at position 0.955 with{\arrow[line width =2pt]{>}}},%{latex}}},
        postaction={decorate}]
        let
        \n1={asin(\gap/2/\bigradius)},
        \n2={asin(\gap/2/\littleradius)}
        in (180-\n1:\bigradius) -- (-180-\n2:\littleradius)
        arc(180-\n2:-180+\n2:\littleradius)--(-180+\n1:\bigradius)
        arc(-180+\n1:-90:\bigradius)--(3,-4)--(3,4)--(0,4)arc(90:(180-\n1):\bigradius);
        \coordinate (T) at (135:2); \node[above] at (T){$T$}; 
        \coordinate (H) at (1.5*\bigradius,0); \node[below] at (H){\Large\bf {x}};
        \coordinate (J) at (0,1.5*\bigradius); \node[left] at (J){$\Large\bf y$}; 
        \coordinate (C) at (\littleradius,0); \node[below right] at (C) {\Large\bf {C}};
        \coordinate (D) at ({180-asin(\gap/2/\littleradius)}:1); \node[above left] at (D) {$ \Large\bf B$}; 
        \coordinate (E) at ({-180+asin(\gap/2/\littleradius)}:1); \node[below left] at (E) {$\Large\bf D$}; 
        \coordinate (F) at ({180-asin(\gap/2/\bigradius)}:\bigradius); \node[above left] at (F) {$\Large\bf A$}; 
        \coordinate (G) at ({-180+asin(\gap/2/\bigradius)}:\bigradius); \node[below left] at (G) {$\Large\bf  E$}; 
        \coordinate (P) at (0,-4); \node[below right] at (P) {$\Large\bf F$}; \coordinate(Q) at (3,-4); \node[right] at (Q) {$\Large\bf G(\gamma-iT)$}; 
        \coordinate (R) at (3,4); \node[right] at (R) {$\Large\bf H(\gamma+iT)$}; 
        \coordinate (S) at (0,4);\node[above right] at (S) {$\Large\bf K$};
        \end{tikzpicture}
\end{document}

ingrese la descripción de la imagen aquí

y esto es lo que estoy buscando: ingrese la descripción de la imagen aquí

Respuesta1

Simplemente cambié el camino para que pase por los puntos.(45:\bigradius)

let
        \n1={asin(\gap/2/\bigradius)},
        \n2={asin(\gap/2/\littleradius)}
        in (180-\n1:\bigradius) -- (-180-\n2:\littleradius)
        arc(180-\n2:-180+\n2:\littleradius)--(-180+\n1:\bigradius)
        arc(-180+\n1:-45:\bigradius)--(45:\bigradius)arc(45:(180-\n1):\bigradius);

captura de pantalla

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.markings,positioning}
\begin{document}
        \begin{tikzpicture}
        %configurable parameters
        \def\gap{0.4}
        \def\bigradius{4}
        \def\littleradius{1}
        %axes
        \draw[line width=2pt,->](-1.5*\bigradius,0) -- (1.5*\bigradius,0)
        (0,-1.5*\bigradius) -- (0,1.5*\bigradius);
        \draw[line width=2pt,->] (0,0)--(45:\littleradius);
        \draw[line width=2pt,->](0,0) -- (135:\bigradius); \node[above
        right] at (45:\littleradius/1.5) {\large\bf{$\varepsilon$}};
        \draw[line width=1pt,decoration={markings,
            mark=at position 0.07 with{\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.17 with{\arrow[line width =2pt]{>}},
            mark=at position 0.27 with{\arrow[line width =2pt]{>}},
            mark=at position 0.35 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.47 with{\arrow[line width =2pt]{>}},
            mark=at position 0.53 with{\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.6 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.65 with {\arrow[line width =2pt]{>}},%{latex}},
            mark=at position 0.7 with{\arrow[line width =2pt]{>}},
            mark=at position 0.8 with{\arrow[line width =2pt]{>}},
            mark=at position 0.85 with{\arrow[line width =2pt]{>}},
            mark=at position 0.955 with{\arrow[line width =2pt]{>}}},%{latex}}},
        postaction={decorate}]
        let
        \n1={asin(\gap/2/\bigradius)},
        \n2={asin(\gap/2/\littleradius)}
        in (180-\n1:\bigradius) -- (-180-\n2:\littleradius)
        arc(180-\n2:-180+\n2:\littleradius)--(-180+\n1:\bigradius)
        arc(-180+\n1:-45:\bigradius)--(45:\bigradius)arc(45:(180-\n1):\bigradius);
        \coordinate (T) at (135:2);
         \node[above] at (T){$T$}; 
        \coordinate (H) at (1.5*\bigradius,0);
         \node[below] at (H){\Large\bf {x}};
        \coordinate (J) at (0,1.5*\bigradius);
         \node[left] at (J){$\Large\bf y$}; 
        \coordinate (C) at (\littleradius,0);
         \node[below right] at (C) {\Large\bf {C}};
        \coordinate (D) at ({180-asin(\gap/2/\littleradius)}:1);            \node[above left] at (D) {$ \Large\bf B$}; 
        \coordinate (E) at ({-180+asin(\gap/2/\littleradius)}:1);           \node[below left] at (E) {$\Large\bf D$}; 
        \coordinate (F) at ({180-asin(\gap/2/\bigradius)}:\bigradius); 
        \node[above left] at (F) {$\Large\bf A$}; 
        \coordinate (G) at ({-180+asin(\gap/2/\bigradius)}:\bigradius); 
        \node[below left] at (G) {$\Large\bf  E$}; 
        \coordinate (P) at (0,-4);
        
         \node[below right] at (P) {$\Large\bf F$};
         \coordinate(Q) at (3,-4);
        \node[right] at (Q) {$\Large\bf G(\gamma-iT)$}; 
        \coordinate (R) at (3,4); 
        \node[right] at (R) {$\Large\bf H(\gamma+iT)$}; 
        \coordinate (S) at (0,4);
        \node[above right] at (S) {$\Large\bf K$};
        \end{tikzpicture}
\end{document}

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