1. A computing device, comprising: a processor; a display screen that includes a transmissive layer having a diffractive pattern configured to direct at least a portion of light received over a plurality of angles incident on a plurality of regions of the display screen to a plurality of light sensors near at least one edge of the transmissive layer; and memory including instructions that, when executed by the processor, cause the computing device to: detect intensity values of the at least the portion of light incident on the plurality of regions of the display screen using the plurality of light sensors; analyze variations in the intensity values caused by a shadow on the display screen to determine a difference between a first intensity value corresponding to a first region of the display screen and a second intensity value corresponding to at least a second region of the display screen; and determine a position with respect to the computing device for one or more objects that cast the shadow on the display screen based on one or more characteristics of the first intensity value.