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We report on a virtual environment for natural immersive exploration of extremely detailed surface models on multi-projector light field displays, which give multiple, freely moving, naked-eye viewers the illusion of seeing and manipulating 3D objects with continuous horizontal parallax. Our specialized 3D user interface, dubbed FOX (Focus Sliding Surface), allows inexperienced users to inspect 3D objects at various scales, integrating panning, rotating, and zooming controls into a single low-degree-of-freedom operation. At the same time, FOX takes into account the requirements for comfortable viewing on the light field display hardware, which has a limited field-of-view and a variable spatial resolution. Specialized multi-resolution structures, embedding a fine-grained, per-patch spatial index within a coarse-grained patch-based mesh structure, are exploited for fast batched I/O, GPU-accelerated rendering, and user-interaction-system-related geometric queries. The capabilities of the system are demonstrated by the interactive inspection of a giga-triangle dataset on a large-scale, 35MPixel light field display controlled by wired or vision-based devices. Results of a thorough user evaluation, involving quantitative and subjective measurements, are discussed.