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Strong discontinuities, such as fractures or geological faults, represent one of the main challenges in geological modeling. Among the different approaches in the literature to represent such discontinuities, methods employing non-conforming meshes gained attention recently [1]. However, their application is often limited by the capabilities of the geometric pre-processing tools, especially for complex 3D geometries. This work addresses this critical pre-processing stage, leveraging established computer graphics techniques, including ray tracing [2]. We present a robust geometry pipeline for discontinuities that conforms not only to the mesh, but also to other geometric entities, such as junctions. We provide a high-performance, free software implementation capable of managing complex geometries with multiple discontinuities against arbitrary meshes and element types. The proposed approach was evaluated using several geological models containing multiple discontinuities with junctions, demonstrating its robustness and efficiency in managing intricate geometric configurations. This implementation is a practical solution that overcomes common limitations of previous works imposed by complex geometries.