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\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows}
\usetikzlibrary{intersections}
\usetikzlibrary{math}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{calc}
\begin{document}
\tdplotsetmaincoords{60}{130}
\pgfmathsetmacro{\l}{2}
\begin{tikzpicture}[
>=latex,
tdplot_main_coords,
dot/.style = {
black, fill = black, circle,
outer sep = 0, inner sep = 0,
minimum size = 1mm
},
round/.style = {
draw = orange, thick, circle,
minimum size = 1mm,
inner sep = 0pt, outer sep = 0pt,
},
cross/.style = {
cross out, draw = magenta, thick,
minimum size = 1mm,
inner sep = 0pt, outer sep = 0pt
},
]
% origin
\coordinate (O) at (0,0,0);
% poles
\coordinate (NP) at (0,0,\l);
\coordinate (SP) at (0,0,-\l);
% axis
% \draw[->] (O) -- ++(1.5*\l,0,0);
% \draw[->] (O) -- ++(0,1.5*\l,0);
% \draw[->] (O) -- ++(0,0,1.5*\l);
% gray unit circle
\tdplotdrawarc[gray, thick]{(O)}{\l}{0}{360}{}{};
\draw[gray, dotted] (-\l, 0, 0) to (\l, 0, 0);
\draw[gray, dotted] (0, -\l, 0) to (0, \l, 0);
% meridians
\foreach \phi in {0, 30, 60, ..., 150}{
\tdplotsetrotatedcoords{\phi}{90}{0};
\tdplotdrawarc[lightgray, dashed, tdplot_rotated_coords]{(O)}{\l}{0}{360}{}{};
}
% dot above and its projection
\pgfmathsetmacro{\phi}{120}
\pgfmathsetmacro{\theta}{60}
\pgfmathsetmacro{\px}{cos(\phi)*sin(\theta)*\l}
\pgfmathsetmacro{\py}{sin(\phi)*sin(\theta)*\l}
\pgfmathsetmacro{\pz}{cos(\theta)*\l})
\coordinate (A) at (\px,\py,\pz);
\coordinate (Aproj) at ({\px * \l / (\l + \pz)}, {\py * \l / (\l + \pz)}, 0);
% dot below and its projection
\pgfmathsetmacro{\phi}{-60}
\pgfmathsetmacro{\theta}{120}
\pgfmathsetmacro{\px}{cos(\phi)*sin(\theta)*\l}
\pgfmathsetmacro{\py}{sin(\phi)*sin(\theta)*\l}
\pgfmathsetmacro{\pz}{cos(\theta)*\l})
\coordinate (B) at (\px,\py,\pz);
\coordinate (Bproj) at ({\px * \l / (\l - \pz)}, {\py * \l / (\l - \pz)}, 0);
% projection lines
\draw[gray] (A) to (SP);
\draw[gray] (SP) to (O) to (Aproj);
\draw[gray] (B) to (NP);
\draw[gray] (NP) to (O) to (Bproj);
% dots
\draw (O) node[dot] {};
\draw (SP) node[dot] {};
\draw (NP) node[dot] {};
\draw (A) node[dot, fill = magenta, minimum size = 1.5mm] {};
\draw (B) node[dot, fill = orange, minimum size = 1.5mm] {};
% projection markers
\draw[very thick, magenta]
(Aproj) ++(.15,0) to ($(Aproj)+(-.15, 0)$)
(Aproj) ++(0,.15) to ($(Aproj) +(0, -.15)$);
\tdplotdrawarc[orange, very thick]{(Bproj)}{.1}{0}{360}{}{};
\end{tikzpicture}
\end{document}
% vim:ts=2 sw=2 et:
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