Morphing Surfaces in GeoGebra AR

KEY QUESTIONS FOR THE FIRST TWO SCREENCASTS:

After the first transformation (in each screencast), cross sections parallel to the plane z = 0 are SQUARES. How can we mathematically justify this for each screencast? For each transformation after the first (in each screencast), are there any regions over the xy-plane for which the surface is UNDEFINED? If so, what are these regions? How can we tell?

MORPHING A PARABOLOID

MORPHING A CONE

KEY QUESTIONS FOR THE NEXT SCREENCAST (BELOW):

After the transformations are completed (for both pyramids), how would you describe regions (over the xy-plane) for which both surfaces are undefined? How do we know this to be true?

MORPHING A SQUARE PYRAMID