How to progressively map a plane to a semisphere?

[PhotoComix]

this is somehow related to this question
http://www.gimptalk.com/forum/%22ben...re-t39911.html

Anyway my qustion may be a bit different:
suppose a plane, as a rectangular and a bit elastic grid,as a net

Now from below the grid ,in its very center a sphere, no larger then the plane, start to pop out,springing upward , pushing up the net

Beyond a certain point of push the elasticity of the net is no sufficient, starting where tension is higher )the net anchors to the plane broke

More the net is free more it wrap around the sphere

But here the difference with the original question, i would like this applied to the Semisphere not to the sphere

meaning that when half of the sphere pop out, the net should be totally wrapped around the surface of the semisphere:

all anchor points previously on the periphery of the rectangle transferred on the Equator, on the maximum circumference of the Sphere, where intersect the plane.

Now you may replace the word "grid" with "original image"
to understand better the point

well i would really like have a similar mapping script and what i found difficult is not map the plane to the semi-sphere but all the "in betweens", the progression

I believe a script for Mathmap will be the easier and more handy solution (as name said is a gimp plugin created for mapping, and ,bigger point support animation and customized script )

But anyway if that may solved by a gimp script or plugin would be the same till the output may be a animation.

I just think that MathMap, and soon GMIC offer a easier and more flexible solution,and what relevant a good preview of the results, but even as a gimp script will be handy

But i'm not good to write scripts, even less in this case because i can't figure out a formula for a similar mapping

I just hope cartographers may ,if not actually code (will be the best ) found the formula to be applied