How to confine light energy associated with surface plasmon polaritons (SPPs) in a physical space with minimal radiation loss whereas creating maximum interacting section with surrounding environment is of particular interest in plasmonic optics. By virtue of transformation optics, we propose a design method of forming a polygonal surface-plasmonic resonator in fully open structures by applying the nonmagnetic affine transformation optics strategy. The radiation loss can be suppressed because SPPs that propagate in the designed open structures will be deceived as if they were propagating on a flat metal/dielectric interface without radiation. Because of the nonmagnetic nature of the transformation strategy, this design can be implemented with dielectric materials available in nature. An experimentally verifiable model is subsequently proposed for future experimental demonstration. Our design may find potential applications in omnidirectional sensing, light harvesting, energy storage and plasmonic lasing.