BoundingBox

A bounding box is a simple geometric figure used to enclose a set of points or a geometric object. In two dimensions it is a rectangle, and in three dimensions it is a rectangular prism. Two common forms are axis-aligned bounding boxes (AABB), whose faces are parallel to the coordinate axes, and oriented bounding boxes (OBB), which may be rotated.

Representation and computation: In 2D an AABB is typically stored as (min_x, min_y, max_x, max_y), from which width and height can be derived. In 3D an AABB uses (min_x, min_y, min_z, max_x, max_y, max_z). An OBB can be represented by its center, three extents, and a rotation matrix or quaternion. To obtain a bounding box from a set of points, compute the minimum and maximum coordinates along each axis. For a mesh, include all vertex coordinates, optionally after applying a transformation.

Applications: Bounding boxes are used to define object locations in images, for image cropping and fast object localization. They are also essential in collision detection in games and physics engines, in view frustum culling in graphics, and in spatial indexing and queries in geographic information systems.

Limitations: Axis-aligned boxes can be loose around rotated shapes, reducing their usefulness for tight fitting or precise collision tests. Oriented bounding boxes are more accurate but require more computation to construct and test. Bounding boxes do not capture the full detail of object shapes beyond their enclosing volume.