# Drawing a projection onto a sphere with Tikz

I am creating a document explaining the concept of a solid angle in Astronomy to students. I would like to create a graphic as shown below in TikZ to illustrate the concept clearly, but I have no idea where to start. It is supposed to illustrate a sphere of radius r and a solid D whose projection onto the sphere gives the area A. Any help is appreciated!

• Surely we have done this already? tex.stackexchange.com/questions/108915/… – Thruston Jul 9 '18 at 9:17
• The lines of projection and labelling of the solid before projection are not present, and the formatting is quite different since my solid is outside the sphere. – Teyyf Jul 9 '18 at 9:52
• All you need to do is to draw a circle on a sphere. This can be done with pgfplots or without. – marmot Jul 9 '18 at 10:25

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{backgrounds}
\usepackage{tikz-3dplot}

\makeatletter

%along z axis
\define@key{z sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{z sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{z spherical visible}{%
\setkeys{z sphericalkeys}{#1}%
\pgfmathsetmacro{\Xtest}{cos(90-\tdplotmaintheta)*cos(\tdplotmainphi-90)*cos(\mytheta)*cos(\myphi)
+cos(90-\tdplotmaintheta)*sin(\tdplotmainphi-90)*cos(\mytheta)*sin(\myphi)
+sin(90-\tdplotmaintheta)*sin(\mytheta)}
% \Xtest is the projection of the coordinate on the normal vector of the visible plane
\pgfmathsetmacro{\ntest}{ifthenelse(\Xtest<0,0,1)}
\ifnum\ntest=0
\else
\fi
}

\tikzdeclarecoordinatesystem{z spherical invisible}{%
\setkeys{z sphericalkeys}{#1}%
\pgfmathsetmacro{\Xtest}{cos(90-\tdplotmaintheta)*cos(\tdplotmainphi-90)*cos(\mytheta)*cos(\myphi)
+cos(90-\tdplotmaintheta)*sin(\tdplotmainphi-90)*cos(\mytheta)*sin(\myphi)
+sin(90-\tdplotmaintheta)*sin(\mytheta)}
% \Xtest is the projection of the coordinate on the normal vector of the visible plane
%\typeout{\raarot,\rbarot,\rabrot,\rbbrot,\racrot, \rbcrot}
\pgfmathsetmacro{\ntest}{ifthenelse(\Xtest<0,0,1)}
\ifnum\ntest=1
\else
\fi
}

%%%%%%%%%%%%%%%%%

\makeatother
% decoration
\begin{document}

\foreach \X in {30}
{\begin{tikzpicture}

\tdplotsetmaincoords{110}{\X}
\begin{scope}[tdplot_main_coords,samples=60]
%
% phi={\tdplotmainphi-90},theta={90-\tdplotmaintheta});
% \draw[-latex] (0,0,0) -- (\RadiusSphere,0,0) node[below]{$x$};
% \draw[-latex] (0,0,0) -- (0,\RadiusSphere,0) node[left]{$y$};
% \draw[-latex] (0,0,0) -- (0,0,\RadiusSphere) node[left]{$z$};
\pgfmathtruncatemacro{\Dis}{ifthenelse(\X<50,1,0)+ifthenelse(\X>130,1,0)}
\ifnum\Dis=0
\else
\draw[opacity=0.3,fill opacity=0.2,fill=blue] plot[smooth,variable=\x,domain=-180:180]
\fi

\pgfmathtruncatemacro{\Dis}{ifthenelse(\X<230,1,0)+ifthenelse(\X>320,1,0)}
\ifnum\Dis=0
\else
\draw[fill opacity=0.5,fill=blue] plot[smooth,variable=\x,domain=-180:180]
\fi
\coordinate (CT) at (z spherical visible cs:
\coordinate (CB) at (z spherical visible cs:
% \draw[gray] plot[smooth,variable=\x,domain=-180:180]