In radiofrequency ion traps, electric fields are produced by applying time-varying potentials between machined metal electrodes. The electrode shape constitutes a boundary condition and defines the field shape. This paper presents a new approach to making ion traps in which the electrodes consist of two ceramic discs, the facing surfaces of which are lithographically imprinted with sets of concentric metal rings and overlaid with a resistive material. A radial potential function can be applied to the resistive material such that the potential between the plates is quadrupolar, and ions are trapped between the plates. The electric field is independent of geometry and can be optimized electronically. The trap can produce any trapping field geometry, including both a toroidal trapping geometry and the traditional Paul-trap field. Dimensionally smaller ion trajectories, as would be produced in a miniaturized ion trap, can be achieved by increasing the potential gradient on the resistive material and operating the trap at higher frequency, rather than by making any physical changes to the trap or the electrodes. Obstacles to miniaturization of ion traps, such as fabrication tolerances, surface smoothness, electrode alignment, limited access for ionization or ion injection, and small trapping volume are addressed using this design.