Q:How to Transform Geometry & Maintain Volume

Hey fellow grasshoppers,

I have a specific question about creating a parametric model which makes it possible to transform its geometry and at the same time to maintain its volume.

The idea is similar to a balloon where by force the form can change but the volume is the same. In the attachment you can find a diagram of what  I want to achieve and a very basic grasshopper model. The only constrain I have is the four anchor points that you see in the illustration. The transformation needs to be outside this this anchor points. Please see the attachment to have a complete image of what I ask. 

I tried to use kangaroo2 but I couldn't manage to create the desired result.

Thanks in advance for your energy.

Best regards,

Alexis