Deform to disk: Paraview versus Matlab

The problem is defined as follows: Given the domain of unit square Ω = [0,1]x[0,1] find the displacement field u(x,y) that deforms the square into a quarter of the disk, with the radius of the disk equal the length of square diagonal.

Definition of the displacement field and subsequent visualization can be one at once in ParaView. To recrete image shown below you can load the following ParaView state file.