Recent research has demonstrated that neural networks using periodic nonlinearities may be used for implicit representation and reconstruction of continuous-time signals. Starting with a previously published network for representing the Signed Distance Function (SDF) of a mesh surface, we extend the concept and lay the foundation for introducing the additional representation of the Unit Normal Function (UNF). With the representation of these two functions at hand, we construct a penalty-based haptic rendering method. Our experiments suggest that this proposed method is able to handle very large meshes better than other competing alternatives, producing high-fidelity forces, free of discontinuities, by sampling a continuous implicit force function at the desired spatial accuracy.