In this paper we introduce a novel approach for stereoscopic rendering of virtual environments with a wide Field-of-View (FoV) up to 360°. Handling such a wide FoV implies the use of non-planar projections and generates specific problems such as for rasterization and clipping of primitives. We propose a novel pre-clip stage specifically adapted to geometric approaches for which problems occur with polygons spanning across the projection discontinuities. Our approach integrates seamlessly with immersive virtual reality systems as it is compatible with stereoscopy, head-tracking, and multi-surface projections. The benchmarking of our approach with different hardware setups could show that it is well compliant with real-time constraint, and capable of displaying a wide range of FoVs. Thus, our geometric approach could be used in various VR applications in which the user needs to extend the FoV and apprehend more visual information.