boundingvolume

A bounding volume is a simple geometric primitive that completely contains a more complex object or scene. It is used to perform fast, coarse computations for queries such as intersection tests, visibility determinations, distance estimation, and collision detection. Bounding volumes are commonly employed in computer graphics, physics engines, robotics, and geographic information systems. They can be static or updated dynamically as objects move.

Common types include axis-aligned bounding boxes (AABBs), defined by minimum and maximum coordinates along each axis; oriented bounding boxes (OBBs), which are not restricted to axis alignment and can fit objects more tightly; bounding spheres, defined by a center and radius; and bounding capsules or cylinders. The set also includes k-DOPs (k-discrete oriented polytopes), which generalize box-like shapes using a fixed set of directions. Bounding volumes can be arranged in hierarchies, such as bounding-volume hierarchies (BVHs) or k-d trees, to accelerate spatial queries by grouping primitives under enclosing envelopes.

Construction and queries typically involve fitting a volume to the geometry and updating it as needed in dynamic scenes. Intersections between bounding volumes are tested with simple algorithms: AABB–AABB and sphere–sphere tests are straightforward, while AABB–sphere and OBB–OBB tests may use the separating axis theorem to determine overlap. In broad-phase collision detection, bounding volumes prune many non-colliding pairs before more expensive narrow-phase checks are performed.

Applications include frustum culling and occlusion testing in rendering, broad-phase collision detection in physics simulations, and acceleration structures in ray tracing. Bounding volumes also support spatial queries and planning in robotics, enabling efficient collision avoidance and environment analysis.