I'm using some lines of code to "interpolate" between shapes in a nice way in Unity.

Here is the code :
shapeShifter.cs
dualShapeModel.cs
shapeTester.cs

Here is a windows demo.

It only works with shapes whose angular vertex positions are distributed around a point in a linear order.
I'm using Ragespline to display the final shape, but it could work with any 2D vector environment.

gitHub page