An important ambition of the Virtual Cuneiform Project has been the automated reconstruction of cuneiform tablets from virtual fragments. The first successful automatic joins of virtual fragments of cuneiform (from both Uruk and Ur) were achieved using a novel matching method. The matching method works by iteratively finding the best orientation of the two candidate fragments in three-dimensional space. A “cost function” assesses the fit of fragments using the distances between pairs of points evenly distributed across the joining surfaces. These distances are calculated using hardware acceleration provided by the computer’s Graphical Processing Unit (GPU). This speeds up what would otherwise be a long series of computations and enables possible matches to be evaluated in milliseconds for fragment pairs consisting of tens of thousands of vertices and a complete optimisation achieved within a matter of seconds. The matching algorithm is described in detail in our project publications.