Temporally Coherent Hierarchical Distance Queries for Deformable Triangle Meshes

Abstract Signed-distance queries on deformable triangle meshes are fundamental operations that are repeatedly performed in a wide range of applications, including collision handling, surface tracking, physically based simulation, and geometric processing. However, in dynamic environments where a mesh continuously deforms over time, reconstructing a static hierarchy at every frame or updating all bounding volumes can incur substantial computational cost, while conventional distance-query acceleration structures do not fully exploit such temporal coherence. In this paper, we propose a temporally coherent hierarchical distance-query method for deformable triangle meshes. The proposed method maintains an anisotropic temporal bound for each hierarchy node to account for local deformation and selectively refreshes the stored reference bound only for nodes whose deformation magnitude exceeds a prescribed threshold, thereby preserving the tightness of the temporal bounds. In addition, nearest-triangle information from the previous frame is retained as a compact persistent seed and re-evaluated on the deformed geometry of the current frame to obtain a tight initial distance upper bound. A stackless traversal is then performed using conservatively expanded hierarchical bounds to compute the exact nearest triangle and signed distance. This temporal-coherence-based hierarchy reuse and selective refresh strategy effectively reduces the cost of repeated distance queries while preserving accuracy under continuous mesh deformation. Experimental results show that, under identical distance-field resolutions and deformation conditions, the proposed method produces signed-distance values that agree with those of the baseline within numerical precision while improving distance-query performance by up to approximately $2.5\times$ in the evaluated tests. The proposed method can therefore be effectively applied to a broad range of real-time graphics and simulation applications that require repeated distance computations on dynamic and deformable geometry.