This thing is intended for OpenSCAD users who want to design smoothly curved vases without waiting for long rendering times. It includes the OpenSCAD code, the STL file for the default design, and the OpenSCAD customizer file (wave_vase.json) that includes the five other example vase designs shown in these pics.

The OpenSCAD code generates a curved 2D shape, then uses rotate_extrude() to make it 3D. The result is like a linear_extrude() on a polygon with $fn sides, except that instead of extruding along a straight line, it extrudes along a sine wave. One advantage this code has over linear_extrude() is that the walls are the same thickness throughout. When you use the scale parameter with linear_extrude(), wall thickness varies with height. The other advantage of this approach is that it renders much faster.

This program has ten parameters that you can alter to change the shape of the vase. The parameters are:
height = height of the vase
radius = nominal radius of the vase (actual radius at any point depends on other parameters)
wall_thickness = thickness of the sides of the vase
base_thickness = thickness of the base (may be 0)
scale = how much to scale the radius by height, e.g., if the scale is 2, the top will be twice as wide as the bottom
waves = how many sine waves to use to generate the vase's profile (may be 0)
wave_amplitude = the width that the sine wave adds or subtracts from the radius
wave_start_angle = the start point of the sine wave
slices = vertical resolution, setting slices=height works well for most curved designs,
$fn = horizontal resolution, low numbers will make vases with flat sides, 180 will make a smooth circumference