comment to https://tex.stackexchange.com/questions/199161/pa

\documentclass[margin=5pt, tikz]{standalone}
\usepackage{pgfplots}
\usepackage{xxcolor}
\pgfplotsset{compat=1.10}

% Declare nice sphere shading: http://tex.stackexchange.com/a/54239/12440
\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{0bp}{0bp}}{%
 color(0bp)=(tikz@ball!0!white);
 color(7bp)=(tikz@ball!0!white);
 color(15bp)=(tikz@ball!70!black);
 color(20bp)=(black!70);
 color(30bp)=(black!70)}
\makeatother

% Style to set TikZ camera angle, like PGFPlots `view`
\tikzset{viewport/.style 2 args={
    x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},
    y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},
    z={(0,{cos(#2)*1cm})}
}}

% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
}}
\pgfplotsset{only background/.style={
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}

% Automatically plot transparent lines in background and solid lines in foreground
\def\addFGBGplot[#1]#2;{
    \addplot3[#1,only background, opacity=0.25] #2;
    \addplot3[#1,only foreground] #2;
}

\newcommand{\ViewAzimuth}{0}
\newcommand{\ViewElevation}{30}

\begin{document}
\begin{tikzpicture}
    % Compute camera unit vector for calculating depth
    \pgfmathsetmacro{\CameraX}{sin(\ViewAzimuth)*cos(\ViewElevation)}
    \pgfmathsetmacro{\CameraY}{-cos(\ViewAzimuth)*cos(\ViewElevation)}
    \pgfmathsetmacro{\CameraZ}{sin(\ViewElevation)}
    \path[use as bounding box] (-1,-1) rectangle (1,1); % Avoid jittering animation
    % Draw a nice looking sphere
    \begin{scope}
        \clip (0,0) circle (1);
        \begin{scope}[transform canvas={rotate=-20}]
            \shade [ball color=white] (0,0.5) ellipse (1.8 and 1.5);
        \end{scope}
    \end{scope}
    \begin{axis}[
        hide axis,
        view={\ViewAzimuth}{\ViewElevation},     % Set view angle
        every axis plot/.style={very thin},
        disabledatascaling,                      % Align PGFPlots coordinates with TikZ
        anchor=origin,                           % Align PGFPlots coordinates with TikZ
        viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
    ]
         \foreach \i in {10,30,...,350} {
\def\theX{0.5*(1-cos(deg(x)))} % 0 to 1 to 0
\def\theY{0.5*(sin(deg(x))} % 0 to 0.5 to 0 to -0.5 to 0
        \addFGBGplot[domain=0:2*pi, samples=101, samples y=1, red]
        (
            {sin(\i)*\theX}, % X coordinate
            {sin(\i)*\theY}, % Y coordinate
        {1-((1-cos(\i)))*\theX}
        );
        }
    \end{axis}
\end{tikzpicture}
\end{document}