Kdtyjb

I would like to draw a sphere with one handle as follows:

I have tried with the following code from Draw a sphere with a handle with TikZ, but this is different from my required image.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

begin{document}

    tdplotsetmaincoords{70}{110}

    begin{tikzpicture}[tdplot_main_coords]

    path[tdplot_screen_coords,use as bounding box] (-3.2,-3.2) rectangle (6,6);

    pgfmathsetmacro{R}{3}

    pgfmathsetmacro{myang}{20}

    pgfmathsetmacro{angtop}{-80}

    pgfmathsetmacro{angright}{95}

    coordinate (O) at (0,0,0);

    shadedraw [ball color=gray!40,tdplot_screen_coords] (0,0,0) circle(R);

    path 

    ({3*sin(myang)*cos(angright)},{3*cos(myang)},{3*sin(myang)*sin(angright)}) coordinate (P1)

    ({3*sin(myang)*cos(angtop)},{3*sin(myang)*sin(angtop)},{3*cos(myang)}) coordinate (P2);

    draw[right color=white,left color=gray!80,shading angle=300] plot[variable=x,domain=angtop:angtop+180,samples=91]

    ({3*sin(myang)*cos(x)},{3*sin(myang)*sin(x)},{3*cos(myang)})

    to[out=90,in=0,looseness=2] (P1)

    plot[variable=x,domain=angright:angright-180,samples=91]

    ({3*sin(myang)*cos(x)},{3*cos(myang)},{3*sin(myang)*sin(x)})

    to[out=0,in=90,looseness=4] (P2);

    end{tikzpicture}

end{document}

This produces:

How can I draw the required figure which I want?

This answer comes with three codes, the last of which is the most customizable one. I added two more (looseness) parameters, and playing with them allowed me to draw

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{110}

begin{tikzpicture}[tdplot_main_coords,rotate=-60]

%path[tdplot_screen_coords,use as bounding box] (-3.2,-3.2) rectangle (4,4.5);

pgfmathsetmacro{R}{3}

pgfmathsetmacro{myang}{10} % controls the diameter of the handle

pgfmathsetmacro{angtop}{-80}

pgfmathsetmacro{angright}{95}

pgfmathsetmacro{out}{55}

pgfmathsetmacro{LooOne}{5.2}

pgfmathsetmacro{LooTwo}{4.2}

coordinate (O) at (0,0,0);

shadedraw [ball color=gray!40,tdplot_screen_coords] (0,0,0) circle(R);

path 

({R*sin(myang)*cos(angtop)},{R*sin(myang)*sin(angtop)},{R*cos(myang)}) 

coordinate (P2)

({R*sin(myang)*cos(angright)},{-R*sin(myang)*sin(angright)*cos(out)+R*cos(myang)*sin(out)},

{R*cos(myang)*cos(out)+R*sin(myang)*sin(angright)*sin(out)}) 

coordinate (P1);

draw[opacity=0.5,

right color=white,left color=gray!40!white,shading angle={-225+(90-out)/2}] 

plot[variable=x,domain=angtop:angtop+180,samples=91]

({3*sin(myang)*cos(x)},{3*sin(myang)*sin(x)},{3*cos(myang)})

to[out=90,in=90-out,looseness=LooOne] (P1)

plot[variable=x,domain=angright:angright-180,samples=91]

({R*sin(myang)*cos(x)},{-R*sin(myang)*sin(x)*cos(out)+R*cos(myang)*sin(out)},

{R*cos(myang)*cos(out)+R*sin(myang)*sin(x)*sin(out)}) 

to[out=90-out,in=90,looseness=LooTwo] (P2);

draw[dashed] plot[variable=x,domain=angtop:angtop-180,samples=91]

({3*sin(myang)*cos(x)},{3*sin(myang)*sin(x)},{3*cos(myang)})

plot[variable=x,domain=angright:angright+180,samples=91]

({R*sin(myang)*cos(x)},{-R*sin(myang)*sin(x)*cos(out)+R*cos(myang)*sin(out)},

{R*cos(myang)*cos(out)+R*sin(myang)*sin(x)*sin(out)});

shadedraw [ball color=gray!50,opacity=0.5]

plot[variable=x,domain=angtop:angtop+180,samples=91]

({3*sin(myang)*cos(x)},{3*sin(myang)*sin(x)},{3*cos(myang)})

to[out=90,in=90-out,looseness=LooOne] (P1)

plot[variable=x,domain=angright:angright-180,samples=91]

({R*sin(myang)*cos(x)},{-R*sin(myang)*sin(x)*cos(out)+R*cos(myang)*sin(out)},

{R*cos(myang)*cos(out)+R*sin(myang)*sin(x)*sin(out)}) 

to[out=90-out,in=90,looseness=LooTwo] (P2);

end{tikzpicture}

end{document}