In the past decade, multi-touch-sensitive interactive surfaces have transitioned from pure research prototypes in the lab, to commercial products with wide-spread adoption. One of the longer term visions of this research follows the idea of ubiquitous computing, where everyday surfaces in our environment are made interactive. However, most of current interfaces remain firmly tied to the traditional flat rectangular displays of the today’s computers and while they benefit from the directness and the ease of use, they are often not much more than touch-enabled standard desktop interfaces.
In this paper, we argue for explorations that transcend the traditional notion of the flat display, and envision interfaces that are curved, three-dimensional, or that cross the boundary between the digital and physical world. In particular, we present two research directions that explore this idea: (a) exploring the three-dimensional interaction space above the display and (b) enabling gestural and touch interactions on curved devices for novel interaction possibilities. To illustrate both of these, we draw examples from our own work and the work of others, and guide the reader through several case studies that highlight the challenges and benefits of such novel interfaces. The implications on media requirements and collaboration aspects are discussed in detail, and, whenever possible, we highlight promising directions of future research. We believe that the compelling application design for future non-flat user interfaces will greatly depend on exploiting the unique characteristics of the given form factor.