Summary

Create fluted solids with arbitrary profiles, swirls and more.
You must have access to Rhino3D and its Grasshopper programming plugin for this to work for you.
The video (http://youtu.be/U4JKHKbO-M4) shows how profile and parameter changes allow you to create any model you can imagine

Instructions

Grasshopper allows you to take 3D geometry and other input and process it with great flexibility. The downloadable ZIP file includes a Rhino3D model as an example and an accompanying Grasshopper programme file.

The grasshopper code expects an arbitrary vessel profile. It then creates a series of of fluted sections that are lofted to create the object. The top and bottom sections are mandatory but you can also specify intermediate sections and specify where they are located on the profile curve. At the moment the code has two intermediate sections that can be enabled or disabled at will. By duplicating the section code block you can add as many as you like...
For each section you can specify the number of flutes, the degree of the curve (sharp or smoother), the offsets between the inside and outside of the flute, the rotation of the section and much more. Just play with the parameter sliders and watch what happens to the model. The video provides some hints..

The code will also generate a solid model from the lofted shell - where this is possible. There is a separate parameter block to specify wall and base thickness. This will not always work well with larger wall thicknesses and order 1 flutes as the Grasshopper offset function can "misbehave" and or create interior walls that are invalid.
For this reason you can export either the solid or the vessel outer skin (and base). If you export the latter, then you can either design your own inner wall - or use a slicer like Simplify3D to just print a single layer (helical) vase. (A fast option for objects where a single wall will do!)

A number of examples are depicted and included as STLs. You are genuinely only limited by your imagination. The example file includes a vessel profile in one plane - but if you create this in 3D you will find even more amazing things can be created...

Parametric Vase & Bowl designer