Unmanned Aerial Vehicle (UAV) mounted Base Stations (UAV-BSs) provide flexible coverage for temporary hotspot scenarios; however, efficiently optimizing 3D deployment to satisfy heterogeneous user distributions remains a significant challenge. While Deep Reinforcement Learning (DRL) approaches have shown promise, they often suffer from prohibitive training overhead and poor generalization in cold-start scenarios where the user topology is unknown a priori. To address these limitations, this paper proposes Satisfaction-driven Coverage Optimization via Perimeter Extraction (SCOPE), which is a deterministic and training-free 3D deployment framework. Unlike existing heuristics that rely on fixed-altitude assumptions, SCOPE integrates a perimeter-based peeling strategy with the Welzl Smallest Enclosing Circle (SEC) algorithm to dynamically optimize 3D positions. Theoretically, we provide a rigorous convergence proof and derive a polynomial time complexity of $O(N^2 \log N)$, ensuring predictable execution for real-time applications. Experimentally, we evaluate SCOPE in unpredictable hotspot environments against both traditional heuristics and state-of-the-art DRL baselines under a matched hardware budget. Simulation results demonstrate that SCOPE maintains a high user satisfaction rate between 82% and 88% while generating solutions within millisecond-level latency on commodity hardware. Furthermore, SCOPE demonstrates exceptional resilience by maintaining an approximate 40% functional coverage rate at a minimum altitude constraint of 60 m; in this challenging regime, baseline methods suffer a significant performance degradation, dropping to approximately 20% due to altitude-induced path loss. These findings validate SCOPE as a robust and agile solution for establishing instantaneous digital lifelines in zero-day disaster response missions.

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