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In a paper I am in the process of writing in LaTeX, I need to draw and incorporate some diagrams of hyperbolic surfaces in my LaTeX document. Is there any software I can use to draw hyperbolic surfaces, either closed, or with boundaries or punctures ? Are there any such freely downloadable softwares that I can use to draw such diagrams ? Please let me know if you know one. I apologize if this is off-topic. Thank you !

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When you are writing in LaTeX, basically there is a package for everything. Especially for plotting there is the beautiful pgfplots package: http://pgfplots.sourceforge.net/

Here's an example:

\begin{figure}[h!t]
\centering
%%% Declare tikspicture enviroment %%%
\begin{tikzpicture}
    %%% Declare axes %%%
    \begin{axis}[axis background/.style={fill=blue!10}]
    %%% Declare 3D surface, work on samples to adjust the quality %%%
    \addplot3[surf,domain=0:360,samples=40]
        {sin(x)*sin(y)};
    \end{axis}
\end{tikzpicture}
\end{figure}

Which gives as result: enter image description here

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