I'd like to call attention to the fact that parametric_plot3d cannot plot curves (or surfaces) that include complex values. This is despite that it's documentation states that:

By default for a curve any points where fx, fy, or fz do not evaluate to a real number are skipped.

for example:

var('u v')
parametric_plot3d((u,0,sqrt(1-u^2)),(u,-1,1))

will work, but

parametric_plot3d((u,0,sqrt(1-u^2)),(u,-1,2))

will not (I would expect them to produce identical curves).

Also, surfaces could benefit from ignoring complex values, for example:

parametric_plot3d((u,0,sqrt(1-u^2-v^2)),(u,-1,1),(v,-1,1)).show(aspect_ratio=(1,1,1))

should draw half a sphere.

thanks

Oscar

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