I'd like to deform it using a cage like you would do in Photoshop.
This is done in Photoshop:

When I try to use the point deform node in Hou, the result looks bad

Problems:
1) the deformed shape is not smooth
2) not all 4 sides of the cage touch the deformed ellipse
3) the deformed shape doesn't seem to lay on the plane of the cage
4) the deformed shape trespasses the cage
Any help is super welcome!
Thanks
Attached you'll find the .hip file if you want to have a look.