plot a surface using plot3d etc within a sphere

Question

I recently need to plot a 3d function that satisfies certain constraints, like

x^2+y^2+z^2<=1

or things similar. So I wonder how to plot the part that only lies within the constraints?

An example surface can be

z=x^2-y^2

More interestingly, is it possible to do that for an implicit function, e.g. x^2+y^2-z^3-z=0, without solving for the equation? Thanks a lot!

$\begingroup$ Use RegionFunction to restrict the region of a plot $\endgroup$
– Simon Woods
Jan 16, 2017 at 21:44 — Simon Woods, Jan 16, 2017 at 21:44
$\begingroup$ @SimonWoods Thanks! $\endgroup$
– larry
Jan 17, 2017 at 2:36 — larry, Jan 17, 2017 at 2:36

Marchi · Accepted Answer · 2017-01-16 22:12:28Z

3

@SimonWoods hit the nail on the head here:

Plot3D[x^2 - y^2, {x, -1, 1}, {y, 0 - 1, 1}, 
 RegionFunction -> Function[{x, y, z}, x^2 + y^2 + z^2 <= 1]]

Or with your implicit surface:

ContourPlot3D[
 x^2 + y^2 + z^2 - z == 0, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 RegionFunction -> Function[{x, y, z}, x^2 + y^2 + z^2 <= 1]]

answered Jan 16, 2017 at 22:06

Marchi

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$\begingroup$ Hi, it works great, thanks! $\endgroup$
– larry
Jan 17, 2017 at 2:36

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