# Chebyshev net in the Sphere and Catenary

Hello I have experience writing texts in latex, but I am a beginner in drawing in latex, I have tried to make these graphics with great effort but I have not succeeded. \documentclass[crop,tikz]{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{tikz-3dplot}
\usepackage{amsmath}
\usepackage{amssymb}

\usepgfplotslibrary{fillbetween}

\def \plotwidth {510.0pt}

\definecolor{color0}{RGB}{0,153,216}

\pgfplotsset{compat=1.12}
\pgfplotsset{ticks=none}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
view/h=45,
axis equal,
axis lines=center,
]
\addplot3[surf, opacity=0.5, samples=30, domain=-1:1, y domain=0:2*pi, z buffer=sort] ({sqrt(1-x^2) * cos(deg(y))}, {sqrt( 1-x^2 ) * sin(deg(y))}, x);
\end{axis}
\end{tikzpicture}
\end{document}


I'm sorry for all the inconvenience, I'm just a beginner. I try to make those graphics in RGB={0,153,216}. Thank you very much for all kinds of help, on the other hand if someone knows a book in Portuguese or Spanish to learn how to graph in latex I would appreciate it very much.

• Welcome to TeX.SE! Oct 5, 2021 at 23:13
• I think you should provide more info on Chebyshev net in the Sphere and Catenary, such as formula, or at least some references. Oct 7, 2021 at 15:07
• @BlackMild You're right, I already put it in the same question. Thanks for the observation. Oct 7, 2021 at 15:42
• Obviously, Chebyshev nets is a topic of higher maths. To draw that nets, one has to get some math background (note this is a tex, not math, forum). IMHO, infos that you provide is still not enough to figure/draw out. Do you know exactly the (parameter) equations of these Chebyshev nets ? Consequently, even people with good drawing skills feel difficult to help you. PS: I guess there are a few of people with curious mind (including me ^^) still will try helping when they have long enough free time. Oct 14, 2021 at 6:31
• @BlackMild You are very right, I am going to try to get the equations that define them. In principle it would be to graph a PDE, but I will do the calculations to make it explicit. Oct 15, 2021 at 6:58

This looks like the sphere you gave. But I am pretty sure that this is not a net with equal side lengths.

Perhaps you can point us to a reference with a proper parametrization. The ones I found using google are all in French.

\documentclass[border=9,tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\makeatletter
\def\mdef{\pgfmathsetmacro}
\begin{axis}[height=20cm, view/h=45, axis equal, axis lines=center]
samples=20, domain=-60:60, unbounded coords=jump,
surf, opacity=.7, z buffer=sort,
pre filter/.code={
\edef\u{\pgfplots@current@point@x@unfiltered} % parametric plot's #1
\edef\v{\pgfplots@current@point@y@unfiltered} % parametric plot's #2
\mdef\theta{\u + \v} % azimuth
\mdef\phi{\u - \v} % elevation
\mdef\TooCloseToPole{ \phi > 85 ? 1 : (\phi < -85) ? 1 : 0 }
\if1\TooCloseToPole
\mdef\pgfplots@current@point@z{nan}
\else
\mdef\cosphi{cos(\phi)}
\mdef\pgfplots@current@point@x{\r * \cosphi * cos(\theta)}
\mdef\pgfplots@current@point@y{\r * \cosphi * sin(\theta)}
\mdef\pgfplots@current@point@z{\r * sin(\phi)}
\fi
}
]
(\x, \y, 0);
\end{axis}
\end{tikzpicture}
\end{document} • Thank you very much, you are right, it looks similar but it succeeds if we enlarge the entire sphere. I tried to do it in Mathematica 12, but it didn't work out. I found this (it's in English): cermics.enpc.fr/~massony/slides_defense.pdf Oct 10, 2021 at 7:06