For example, The points
[0, 0, 0],
[40, 60, 0],
[-50, 90, 0] and
[0, 200, 0] would create the Bézier curve below.
The customizer would
translate([bottom_radius, 0, 0]) and
rotate([90, 0, angle]) the curve
fn times. The
angle is calculated from
360 / fn. Then I add a bottom and an optional inner vase.
z coordinate is always
0 so you only need to input
y while using the customizer.
About Bezier vase II
If you want swings in the
z direction, take a look at Bezier vase II.
If you want to know how to create a bezier curve with OpenSCAD, take a look at "Bézier curve".