We introduce apex point map, a simple data structure for constructing conservative bounds for rigid objects. The data structure is distilled from a dense k-DOP, and can be queried in constant time to determine a tight bounding plane with any given normal vector. Both precalculation and lookup can be implemented very efficiently on current GPUs. Applications include, e.g., finding tight world-space bounds for transformed meshes, determining per-object shadow map extents, more accurate view frustum culling, and collision detection.
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