Bounding volume

In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations by using simple volumes to contain more complex objects. Normally, simpler volumes have simpler ways to test for overlap. A bounding volume for a set of objects is also a bounding volume for the single object consisting of their union, and the other way around. Therefore, it is possible to confine the description to the case of a single object, which is assumed to be non-empty and bounded (finite). Bounding volumes are most often used to accelerate certain kinds of tests. In ray tracing, bounding volumes are used in ray-intersection tests, and in many rendering algorithms, they are used for viewing frustum tests. If the ray or viewing frustum does not intersect the bounding volume, it cannot intersect the object contained within, allowing trivial rejection. Similarly if the frustum contains the entirety of the bounding volume, the contents may be trivially accepted without further tests. These intersection tests produce a list of objects that must be 'displayed' (rendered; rasterized). In collision detection, when two bounding volumes do not intersect, the contained objects cannot collide. Testing against a bounding volume is typically much faster than testing against the object itself, because of the bounding volume's simpler geometry. This is because an 'object' is typically composed of polygons or data structures that are reduced to polygonal approximations. In either case, it is computationally wasteful to test each polygon against the view volume if the object is not visible. (Onscreen objects must be 'clipped' to the screen, regardless of whether their surfaces are actually visible.) To obtain bounding volumes of complex objects, a common way is to break the objects/scene down using a scene graph or more specifically a bounding volume hierarchy, like e.g. OBB trees.