Q:

Verb for transforming a sphere into a plane

I'm designing tools for a 3D modeling software. I've programmed two tools – one which turns a cylinder into a straight plane (and back), and another one which turns a sphere into a plane and vice versa. Now I need to know how to call those tools.
The act of transforming a cylinder into a plane can be called unwrapping or unrolling.

» Click to unwrap the cylinder «

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But is there any verb to describe the transformation from a sphere into a plane?

» Click to (?) the sphere «

A:

In math, a surface that can be transformed into a plane is called a developable surface.  Without stretching it, a sphere cannot be directly developed. Same for a saddle curve or a torus (donut shape) . 
So, » Click to develop the sphere «

(Math.)    a surface described by a moving right line, and such that consecutive positions of the generator intersect each other. Hence, the surface can be developed into a plane.

Image of a saddle curve

Reversing the transformation? How about back-developing, globalizing (deliberate humor), rounding out, and orbating or sphering (neologisms)?

