<p>Suppose I have the X, Y, and Z coordinates (either in a list or a function z = f(x,y)) that defines a shape as the one provided and I want to 3D print it with a solid bottom, is there an easy way to do this? If not, how can a functionally well-defined shape be put into a 3D modeling software like FreeCAD?</p>
<p><a href="https://i.stack.imgur.com/5bcSU.jpg" rel="nofollow noreferrer" title="3D graph"><img src="https://i.stack.imgur.com/5bcSU.jpg" alt="3D graph" title="3D graph" /></a></p>

For stuff like this, OpenSCAD is your friend. There are several different approaches you could take:
Generate an image file with grayscale color representing the height of the function on an XY grid, and use the
```
surface
```
feature to import it as a heightmap.
Write the function as a mathematical expression in OpenSCAD language, and write a module to generate a
```
polyhedron
```
by iterating over a sufficiently fine coordiante grid, sampling the function, and producing points and triangles.
Use a library someone else has already written for this purpose. I'm not aware of specific ones but pretty sure there are quite a few.