Prior work in RF-based positioning has mainly focused on discovering the absolute location of an RF source, where state-of-the-art systems can achieve an accuracy on the order of tens of centimeters using a large number of antennas. However, many applications in gaming and gesture based interface see more benefits in knowing the detailed shape of a motion. Such trajectory tracing requires a resolution several fold higher than what existing RF-based positioning systems can offer. This paper shows that one can provide a dramatic increase in trajectory tracing accuracy, even with a small number of antennas. The key enabler for our design is a multi-resolution positioning technique that exploits an intrinsic tradeoff between improving the resolution and resolving ambiguity in the location of the RF source. The unique property of this design is its ability to precisely reconstruct the minute details in the trajectory shape, even when the absolute position might have an offset. We built a prototype of our design with commercial off-the-shelf RFID readers and tags and used it to enable a virtual touch screen, which allows a user to interact with a desired computing device by gesturing or writing her commands in the air, where each letter is only a few centimeters wide.