Creating a 3D shape from layers in Mathematica

In Mathematica, I would like to create a 3-D solid shape. The shape is defined by several different horizontal cross-sections at equal vertical intervals. The shape of each section is defined by a set of points along its outer border. How can I create a smooth 3-D solid shape from the collection of these horizontal cross-sections? The transition of the solid between these cross-sections should be smooth. I have prepared a sample file that shows graphical examples of different sections from which the solid is to be created. Is there a way to attach a doc file? The examples shows 4 sample sections, but the program should be expandable to more sections. The connection between the sections must be smooth, no straight lines. Required is the Mathematica code to achieve creating a 3D shape from layers successfully. Must be in Mathematica.