I am trying to find (or maybe create) an algorithm for creating a smooth, rounded 3D mesh given a 2D outline. I'm trying to recreate a system from a Gamecube game called Amazing Island, and you can see an example of how it works here. A more modern example of what I'm trying to do would be the Soft Edge 3D Doodle tool in Paint 3D.
Basically, you draw a shape with a freeform pen tool, and the shape is "inflated" into a 3D mesh. The result should have smooth, curved, somewhat organic-looking edges, rather than simply extruding the shape into a prism. Each shape can be assumed to be simply connected (meaning shapes with holes through them are not possible), and it can be assumed that the outline won't self-intersect. It would be nice if I could find a way to have non-simply connected shapes, but it's not necessary, and seems like it would be significantly more complicated.
The closest thing that I've been able to find is how to take an outline and triangulate it to make a flat 2D mesh. I'm pretty lost on how I can take that and turn it into what I want though. I can get a list of points representing the vertices of the outline, which seems like it should be the first step.
I'm implementing this in C#, in Unity, but I'm not necessarily looking for code. A description of an algorithm, or even a good idea for how I could approach the problem, would be great. Thank you for your time.