Long-horizon object-centered tasks in interactive 3D environments involve heterogeneous events that unfold across time and space, including fine-grained manipulations, larger structural motions, and subtle state transitions. Effectively visualizing such processes is essential for helping users understand how actions lead to outcomes over time. However, existing camera control methods in 3D systems are commonly designed for static objects, and often fail to maintain the legibility of task-relevant components and their evolving relationships throughout long-horizon executions. We present VISTA, a differentiable viewpoint planning framework for long-horizon task visualization. We formulate camera control as a visualization policy that optimizes camera parameters under a unified rendering-based quality objective and we propose five quality metrics to satisfy our five design goals. To support both local part inspection and interaction-centric visualization centered on a primary object, our formulation handles targets defined either as object--part pairs or as relational tuples involving another interacting object. This allows the planner to reveal not only what part is important, but also how it functionally relates to surrounding structures during task execution. We demonstrate that the same planner supports two complementary use cases: presentation-driven narrative visualization for communicating how long-horizon tasks unfold to human viewers, and agent-driven active observation within an observe-act loop. Together, these results position differentiable viewpoint planning as a general mechanism for ``how-things-work'' visualization of long-horizon object-centered interactions in 3D environments.

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