We present FlexSense, a new thin-film, transparent sensing surface based on printed piezoelectric sensors, which can reconstruct complex deformations without the need for any external sensing, such as cameras. Done in collaboration with Media Interaction Lab, Hagenberg, Austria, and the Institute of Surface Technologies and Photonics, Joanneum Research, FlexSense provides a fully self-contained setup which improves mobility and is not affected from occlusions. Using only a sparse set of sensors, printed on the periphery of the surface substrate, we devise two new algorithms to fully reconstruct the complex deformations of the sheet, using only these sparse sensor measurements. An evaluation shows that both proposed algorithms are capable of reconstructing complex deformations accurately. We demonstrate how FlexSense can be used for a variety of 2.5D interactions, including as a transparent cover for tablets where bending can be performed alongside touch to enable magic lens style effects, layered input, and mode switching, as well as the ability to use our device as a high degree-of-freedom input controller for gaming and beyond.