Plot surface and normal vector fields

Question

I was wondering if there is an easy way to plot a mesh diagram of a surface and also its normal vector field?

For example: I wish to plot the sphere $x^2 + y^2 + z^2 = 1$ and the normal vector field at will be all vectors joining (x,y,z) to (2x,2y,2z), where (x,y,z),lies on the sphere.tiks

Answer 1

This is just for fun and builds on this answer for the background check as well as this answer.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{calc}

\pgfplotsset{compute projections/.code=\pgfmathsetmacro{\CameraX}{sin(\pgfkeysvalueof{/pgfplots/view/az})*cos(\pgfkeysvalueof{/pgfplots/view/el})}
\pgfmathsetmacro{\CameraY}{-cos(\pgfkeysvalueof{/pgfplots/view/az})*cos(\pgfkeysvalueof{/pgfplots/view/el})}
\pgfmathsetmacro{\CameraZ}{sin(\pgfkeysvalueof{/pgfplots/view/el})},
only foreground/.style={compute projections,
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
},only background/.style={compute projections,
    restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    domain=-1:1,
    samples=10,
    xmin=-1.5,xmax=1.5,
    ymin=-1.5,ymax=1.5,
    zmin=-1.5,zmax=1.5,
    ]
      \addplot3[,quiver,-stealth,only background,%opacity=0.1,
      domain=0:360,domain y=-90:90,point meta=1,
      quiver={
        u={x/sqrt((x)^2+(y)^2+(z)^2)},
        v={y/sqrt((x)^2+(y)^2+(z)^2)},
        w={z/sqrt((x)^2+(y)^2+(z)^2)},
        colored,scale arrows=0.5}]
      ({cos(y)*cos(x)},{-cos(y)*sin(x)},{sin(y)});
    %}
    \draw[ball color=gray] let \p1=($(0,0,1.75)-(0,0,0)$) in
     (0,0,0) circle[radius=\y1];
      \addplot3[quiver,-stealth,only foreground,%opacity=0.1,
      domain=0:360,domain y=-90:90,point meta=1,
      quiver={
        u={x/sqrt((x)^2+(y)^2+(z)^2)},
        v={y/sqrt((x)^2+(y)^2+(z)^2)},
        w={z/sqrt((x)^2+(y)^2+(z)^2)},
        colored,scale arrows=0.5}]
      ({cos(y)*cos(x)},{-cos(y)*sin(x)},{sin(y)});
  \end{axis}
\end{tikzpicture}

\end{document}