In computational contact mechanics, the gap function plays a central role in the assessment of clearance and penetration between geometric entities, providing essential information for subsequent contact resolution. The use of a Signed Distance Field (SDF) provides a scalar field that characterizes the distance from any point in space to the nearest surface, making it a popular shape representation technique for contact detection [1]. Although several authors have been investigating node-to-SDF contact detection [1, 2], contact detection between two entities, both represented purely as SDFs, remains an open area of investigation. With applications in various computational fields, including granular mechanics, biomechanical multibody dynamics, or accident reconstruction, geometric primitives in R2, such as ellipses, are the main geometries under investigation. Boolean operators are employed to derive a resultant Gap Distance Field (GDF) between entities, addressing sharp discontinuities in the resulting field with smoothing functionals, such as LogSumExp. Findings revealed that the minima of the soft-GDFs are situated along the common normal of minimum distance between entities. The minima were determined through metaheuristic optimization and the gap value retrieved by evaluating the obtained minima at each SDF. References [1] Macklin, M., Erleben, K., M ̈uller, M., Chentanez, N., Jeschke, S., & Corse, Z. Local Optimization for Robust Signed Distance Field Collision. Proceedings of the ACM on Computer Graphics and Interactive Techniques, 3, 1 - 17 (2020). https://doi.org/10.1145/3384538. [2] Lai, Z., Zhao, S., Zhao, J., & Huang L. Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes. Comput. Mech. 70, 763–783 (2022). https://doi.org/10.1007/s00466-022-02220-8.