Gráfica de una superficie usando TikZ

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% Filename: SurfaceArea.tex
% Description: 
% A surface, corresponding to the graph of a function of two variables ($z = f(x, y)$) is shown.
% 
% Date of creation: March, 12th, 2023.
% date of last modification: March, 12th, 2023.
% Autor: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Terms of use:
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\tdplotsetmaincoords{70}{110}
%
\begin{tikzpicture}[tdplot_main_coords,scale=1.5]
	% Definition of the function to be plotted
	\tikzmath{function f(\x,\y) {return 0.5 + 0.75 * cos((\x * \x + \y * \y) r) / sqrt(1.0 + \x * \x + \y * \y) ;};}
	% Domain for the surface plot: from [\xi,\yi] to [\xf,\yf] 
	\pgfmathsetmacro{\xi}{-3.0} 
	\pgfmathsetmacro{\xf}{3.0}
	\pgfmathsetmacro{\yi}{-3.0}
	\pgfmathsetmacro{\yf}{3.0}
	\pgfmathsetmacro{\n}{60} % Number of subintervals 
	\pgfmathsetmacro{\step}{(\xf - \xi) / \n} % size of each subinterval
	% Basically, \step is the length of the horizontal projection of the side of the surface element
	\pgfmathsetmacro{\xsig}{\xi + \step} % Auxiliary [next x]
	\pgfmathsetmacro{\ysig}{\yi + \step} % Auxiliary [next y]
	\pgfmathsetmacro{\xant}{\xf - \step} % Auxiliary [previous value of x (with respect to the final value)]
	\pgfmathsetmacro{\yant}{\yf - \step} % Auxiliary [previous value of y (with respect to the final value)]
	\pgfmathsetmacro{\ejez}{f(0,0) + 1.0} % Length of the z-axis
	%
	\draw[dashed,->] (0,0,0) -- (\xi,0,0); % Negative part of the x-axis
	\draw[dashed,->] (0,0,0) -- (0,\yi,0); % Negative part of the y-axis
	%
	% Region #1: from (\xi, \yi) to (0,\yf)
	%
	\foreach \x in {\xi,\xsig,...,-\step}{
		\foreach \y in{\yi,\ysig,...,\yant}{
			% Coordinates of the vertices of each surface element
			\pgfmathsetmacro{\Ax}{\x}
			\pgfmathsetmacro{\Ay}{\y}
			\pgfmathsetmacro{\Az}{f(\Ax,\Ay)}
			\pgfmathsetmacro{\Bx}{\x + \step}
			\pgfmathsetmacro{\By}{\y}
			\pgfmathsetmacro{\Bz}{f(\Bx,\By)}
			\pgfmathsetmacro{\Cx}{\x + \step}
			\pgfmathsetmacro{\Cy}{\y + \step}
			\pgfmathsetmacro{\Cz}{f(\Cx,\Cy)}
			\pgfmathsetmacro{\Dx}{\x}
			\pgfmathsetmacro{\Dy}{\y + \step}
			\pgfmathsetmacro{\Dz}{f(\Dx,\Dy)}
			\fill[cyan!50,opacity=0.75] (\Ax,\Ay,\Az) -- (\Bx,\By,\Bz) -- (\Cx,\Cy,\Cz) -- (\Dx,\Dy,\Dz) -- cycle;
			\draw[blue,ultra thin] (\Ax,\Ay,\Az) -- (\Bx,\By,\Bz) -- (\Cx,\Cy,\Cz) -- (\Dx,\Dy,\Dz) -- cycle;
		}
	}
	% Draw the coordinate axis
	\draw[thick,->] (0,0,0) -- (\xf+0.5,0,0) node [below left] {\footnotesize$x$};
	\draw[thick,->] (0,0,0) -- (0,\yf+0.5,0) node [right] {\footnotesize$y$};
	\draw[thick,->] (0,0,0) -- (0,0,\ejez) node[above] {$z$}; % Eje z	
	%
	% Region #2: from (0, \yi) to (\xf,\yf)
	%
	\foreach \x in {0.0,\step,...,\xant}{
		\foreach \y in{\yi,\ysig,...,\yant}{
			% Coordinates of the vertices of each surface element
			\pgfmathsetmacro{\Ax}{\x}
			\pgfmathsetmacro{\Ay}{\y}
			\pgfmathsetmacro{\Az}{f(\Ax,\Ay)}
			\pgfmathsetmacro{\Bx}{\x + \step}
			\pgfmathsetmacro{\By}{\y}
			\pgfmathsetmacro{\Bz}{f(\Bx,\By)}
			\pgfmathsetmacro{\Cx}{\x + \step}
			\pgfmathsetmacro{\Cy}{\y + \step}
			\pgfmathsetmacro{\Cz}{f(\Cx,\Cy)}
			\pgfmathsetmacro{\Dx}{\x}
			\pgfmathsetmacro{\Dy}{\y + \step}
			\pgfmathsetmacro{\Dz}{f(\Dx,\Dy)}
			\fill[cyan!50,opacity=0.75] (\Ax,\Ay,\Az) -- (\Bx,\By,\Bz) -- (\Cx,\Cy,\Cz) -- (\Dx,\Dy,\Dz) -- cycle;
			\draw[blue,ultra thin] (\Ax,\Ay,\Az) -- (\Bx,\By,\Bz) -- (\Cx,\Cy,\Cz) -- (\Dx,\Dy,\Dz) -- cycle;
		}
	}
	%
\end{tikzpicture}
%
\end{document}