I wish to give it thickness for it to be 3d -printable and also yet retain the details. (I tried once with constructing a mesh but somehow it lost the graph mapping details and became something else)

There are some thickening for gh. Weaverbird has a mesh thicken component. Pufferfish has a surface thicken component.

But for the purpose of 3d printing it is probably better to use something like Meshlab or Meshmixer because these softwares have more advanced thickening algorithms specifically to avoid self intersection on concave offset areas. They are also quite good for other fixes in the preporation for 3d printing. They are both free softwares.

I’ve printed a number of vase parts with geometry not quite as complex as yours, so this method might work for you:

CAP the ends of your basic shape.

Use ScaleNU to scale down only the X & Y dimensions of (1) above. I use a single slider connected to ScaleNU’s X & Y inputs with a typical value close to 0.98.

Make a large diameter cylinder with height equal to the thickness of the bottom you want your vase to have, and Cap it.

Use SDiff to subtract (3) from (2). That should give you a closed, manifold Brep that is the vase’s inside volume.

Use SDiff to subtract (4) from (1). You should end up with a closed, manifold Brep that is printable.