How can I plot a portion of a surface in a specified region?

Question

I have a parametric surface in 3D. I would like to observe parts of this surface, specifically, the part with z > 0 and the part with x² + y² + z² < c.

A few methods that I tried:

• Naïvely throwing away the rest of the data, for instance setting X[Z<0] = nan etc. Since this does not line up with the parametrization that I chose, it would create ragged edges. Is there some sort of "antialiasing" interpolation options that I can choose? I would be grateful for a pointer to the docs for numpy or plotly.
• Trying to set the alpha of the color scale. This sort of works, it seems to introduce some incorrect rendering. In the picture below, the dark green lump should be at the front of the light green disk. Is there something that I did wrong?

On the other hand, I couldn't locate in the manual a way to set "two dimensional" color scales, so that I can simultaneously set the opacity according to the z value and the hue according to some other quantity of interest. Is this possible?

Is there a convenient method to achieve my goal? Or can I improve my attempts above? Any help is appreciated!