Most of the time, processes like areal gridding or Delaunay triangulation rely on 2D algorithms. As these algorithms are generally used in geomodeling to create 3D geological objects, a link between the 3D datapoints defining these objects and their 2D representation has to be defined. The common practice is to simply apply geometric projections. Nevertheless, when building a faulted structural model, fault surfaces may interfere with the projection directions. This leads to severe complications when complex fault networks have to be taken into account, especially in presence of reverse faults. The method proposed in this study enables one to create faulted horizon surfaces or to perform an extrusion-based faulted reservoir grid creation independently from the fault network complexity. This new approach aims at building a field of curvilinear directions w allowing projections that are consistent with the fault network geometry (i.e. that do not intersect any fault surfaces). Building such a field is equivalent to define a 3D parameterized space (0,u,v,w), associated to the real 3D space, in which all fault surfaces are strictly vertical. This is performed by constraining the w parametric axis to be tangential to the fault surfaces and to the fault-fault contacts. Two different alternative methods have been tested to compute the parametrized space: (1) it can either be fully defined by computing three parametric coordinates (u, v, w) in the whole domain or (2) only partly defined by constructing a vector field at each point tangential to the w parametric axis. Thanks to this parameterization method, more robust and systematic algorithms has been implemented and successfully used to interpolate faulted and folded horizon surfaces from flat triangulated surfaces and to build stratigraphic grids suitable for flow simulators and containing a minimal number of grid blocks truncated by the faults.