OBBsphere

OBBsphere, also known as the circumscribed sphere of an oriented bounding box, is a bounding volume used in computer graphics, collision detection, and spatial queries. Given an oriented bounding box (OBB) defined by a center c, an orientation R, and half-extents hx, hy, hz along its local axes, the OBBsphere is the sphere that exactly circumscribes the box.

The center of the OBBsphere is the same as the OBB's center. Its radius r is the distance from the center to any vertex, that is r = sqrt(hx^2 + hy^2 + hz^2). Because all eight vertices lie at this distance, the sphere contains the entire OBB.

Properties and use: The OBBsphere is rotationally invariant with respect to the OBB orientation and is the smallest sphere that encloses the OBB. It simplifies broad-phase collision checks since many tests reduce to sphere tests. However, for elongated boxes the circumscribed sphere can be loose, reducing culling efficiency compared with tighter bounds such as capsules or the OBB itself.

Variants and terminology: sometimes simply called the circumsphere of the OBB; sometimes referred to as the minimum bounding sphere of the OBB.

See also: Oriented bounding box, Bounding sphere, Circumscribed sphere.