If a surface of revolution such as an archaeological pot is broken into many fragments it is clear that given accurate measurements of all the pieces, one may reconstruct the broken object from its pieces. In a new paper, we describe how to reconstruct surfaces such as these using only their apparent outer contour when viewed from the side. One major benefit of this approach is that the surface may be reconstructed from pieces which may not share a matching boundary. All that is necessary to reconstruct the apparent contour is a set of fragments which, when matched, cover the entire apparent contour of the unknown pot shape.  From the figure below, (a) and (c)  are 3D meshes of 2 fragments from a single pot. Their estimated apparent outer contours are (b) and (d) respectively. The complete profile estimated by matching the apparent contours is shown in (e). Note that the  curve in (e)  may be revolved around the pot's  axis of symmetry (also estimated) to regenerate the a-priori unknown pot outer surface.