$$\DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{#1}}$$
 (%i1) load(draw)$ (%i2) load(eigen)$

This worksheet provides, what the hyperboloid would
being offered.

 (%i3) F(x, y, z) := x^2 -y^2 -z^2 - 5$ (%i4) G(x, y, z) := [ diff(F(x, y, z), x, 1), diff(F(x, y, z), y, 1), diff(F(x, y, z), z, 1) ]$
 (%i5) Gn(x, y, z) := unitvector(G(x, y, z))$ (%i6) IsLit(x, y, z, vLight, vView) := signum( (G(x, y, z) . vLight) * (G(x, y, z) . vView) ) * 0.5 + 0.5$
 (%i7) L(x, y, z, th1, th2) := abs(    Gn(x, y, z) . [sin(th1), -cos(th1), 1] ) * IsLit(x, y, z, [sin(th1), -cos(th1), 1],    [sin(th2), -cos(th2), 1]     )$ (%i8) implObj: implicit(F(x, y, z), x, -10, 10, y, -10, 10, z, -10, 10)$
 (%i9) start: elapsed_real_time()$ (%i10) with_slider_draw3d( f, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0], x_voxel=40, y_voxel=40, z_voxel=40, enhanced3d=[ L(x, y, z, (f+1)*%pi/6, f*%pi/6) * 0.2 + 0.5, x, y, z ], colorbox=false, palette=gray, view = [45, f*30], implObj )$
$\tag{\%{}t10}\label{t10}$

The number of minutes required to plot sequence:

 (%i11) (elapsed_real_time() - start) / 60;
$\tag{\%{}o11}\label{o11} 6.225833333333333$

The machine will OOM, unless it has 12GB of RAM!

Created with wxMaxima.