Efficient visibility computation is a prominent requirement when designing automated camera control techniques for dynamic3D environments; computer games, interactive storytelling or 3D media applications all need to track 3D entities while ensuringtheir visibility and delivering a smooth cinematic experience. Addressing this problem requires to sample a large set of potentialcamera positions and estimate visibility for each of them, which in practice is intractable despite the efficiency of ray-castingtechniques on recent platforms. In this work, we introduce a novel GPU-rendering technique to efficiently compute occlusionsof tracked targets in Toric Space coordinates – a parametric space designed for cinematic camera control. We then rely on thisocclusion evaluation to derive an anticipation map predicting occlusions for a continuous set of cameras over a user-definedtime window. We finally design a camera motion strategy exploiting this anticipation map to minimize the occlusions of trackedentities over time. The key features of our approach are demonstrated through comparison with traditionally used ray-castingon benchmark scenes, and through an integration in multiple game-like 3D scenes with heavy, sparse and dense occluders.