18/01/2026
\documentclass{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\pgfplotsset{colormap={cm}{color(0)=(red) color(1)=(red!90)
color(3)=(red!80) color(4)=(red!70) color(5)=(red!10)}}
\begin{document}
\begin{center}
\begin{tikzpicture}
\begin{axis}[
legend pos=outer north east,
axis lines = middle,
xticklabel style = {font=\tiny},
yticklabel style = {font=\tiny},
zticklabel style = {font=\tiny},
xlabel = $x$,
ylabel = $y$,
zlabel = $z$,
legend style={cells={align=left}},
legend cell align={left},
view={135}{25},
clip=false,
point meta={z-abs(0.2*x+y)}
]
% lower back part
\addplot3[surf,mesh/ordering=y varies,shader=interp,opacity=0.7,
samples=71,samples y=41,domain y=-180:00,domain=-4:1]
({x},{sqrt(1+x*x)*cos(y)},{sqrt(1+x*x)*sin(y)});
\addplot3[ultra thick,color=green,samples=71,samples y=1,
domain=-180:00] ({1},{sqrt(1+1)*cos(x)},{sqrt(1+1)*sin(x)});
% horizontal plane: back
\fill[cyan,opacity=0.4] (1,5,0) -- (1,-5,0) -- (-4.5,-5,0)
-- (-4.5,5,0);
%\addplot3[surf,cyan,domain=-4.5:1,domain y=-5:5,opacity=0.5] {0};
% vertical plane: lower part
\fill[cyan,opacity=0.4] (1,5,0) -- (1,-5,0) -- (1,-5,-5)
-- (1,5,-5);
%\addplot3[surf,cyan,domain=-4.5:0,domain y=-5:5,opacity=0.5] ({1},{y},{x});
% lower front part
\addplot3[surf,mesh/ordering=y varies,
shader=interp,opacity=0.7,samples=71,samples y=41,domain y=-180:00,
domain=1:4] ({x},{sqrt(1+x*x)*cos(y)},{sqrt(1+x*x)*sin(y)});
% horizontal plane: front
\fill[cyan,opacity=0.4] (1,5,0) -- (1,-5,0) -- (5,-5,0)
-- (5,5,0);
%\addplot3[surf,cyan,domain=1:4.5,domain y=-5:5,opacity=0.5] {0};
% upper back part
\addplot3[ultra thick,color=orange,samples=71,samples y=1,
domain=-4:4] ({x},{sqrt(1+x*x)},{0});
\addplot3[ultra thick,color=orange,samples=71,samples y=1,
domain=-4:4] ({x},{-sqrt(1+x*x)},{0});
\addplot3[surf,mesh/ordering=y varies,
shader=interp,opacity=0.7,samples=71,samples y=41,domain y=0:180,
domain=-4:1]
({x},{sqrt(1+x*x)*cos(y)},{sqrt(1+x*x)*sin(y)});
% vertical plane: upper part
\fill[cyan,opacity=0.4] (1,5,0) -- (1,-5,0) -- (1,-5,5)
-- (1,5,5);
\addplot3[ultra thick,color=green,samples=71,samples y=1,
domain=0:180] ({1},{sqrt(1+1)*cos(x)},{sqrt(1+1)*sin(x)});
%\addplot3[surf,cyan,domain=0:4.5,domain y=-5:5,opacity=0.5] ({1},{y},{x});
% upper front part
\addplot3[surf,mesh/ordering=y varies,
shader=interp,opacity=0.7,samples=71,samples y=41,domain y=0:180,
domain=1:4] ({x},{sqrt(1+x*x)*cos(y)},{sqrt(1+x*x)*sin(y)});
\end{axis}
\end{tikzpicture}
\end{center}
\end{document}