Disclosed is a method and system for actively controlling the shape of a sheet of electroactive material; the system comprising: one or more electrodes attached to the frontside of the electroactive sheet; a charged particle generator, disposed so as to direct a beam of charged particles (e.g. electrons) onto the electrode; a conductive substrate attached to the backside of the sheet; and a power supply electrically connected to the conductive substrate; whereby the sheet changes its shape in response to an electric field created across the sheet by an accumulation of electric charge within the electrode(s), relative to a potential applied to the conductive substrate. Use of multiple electrodes distributed across on the frontside ensures a uniform distribution of the charge with a single point of e-beam incidence, thereby greatly simplifying the beam scanning algorithm and raster control electronics, and reducing the problems associated with "blooming". By placing a distribution of electrodes over the front surface of a piezoelectric film (or other electroactive material), this arrangement enables improved control over the distribution of surface electric charges (e.g. electrons) by creating uniform (and possibly different) charge distributions within each individual electrode. Removal or deposition of net electric charge can be affected by controlling the secondary electron yield through manipulation of the backside electric potential with the power supply. The system can be used for actively controlling the shape of space-based deployable optics, such as adaptive mirrors and inflatable antennae.