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On traditional tables, people frequently use the third dimension to pile, sort and store objects. However, while effective and informative for organization, this use of the third dimension does not usually extend far above the table. To enrich interaction with digital tables, we present the concept of shallow-depth 3D -- 3D interaction with limited depth. Within this shallow-depth 3D environment several common interaction methods need to be reconsidered. Starting from any of one, two and three touch points, we present interaction techniques that provide control of all types of 3D rotation coupled with translation (6DOF) on a direct-touch tabletop display. The different techniques exemplify a wide range of interaction possibilities: from the one-touch technique, which is designed to be simple and natural, but inherits a degree of imprecision from its simplicity; through to three-touch interaction, which allows precise bimanual …