aabb

AABB is an acronym with several meanings; in computer graphics and computational geometry, it most commonly denotes an axis-aligned bounding box, a simple volume that encloses a geometric object with faces parallel to the coordinate axes.

In 2D, an AABB is defined by the minimum and maximum coordinates along each axis: xmin, xmax, ymin, ymax, representing the rectangle [xmin, xmax] × [ymin, ymax]. In 3D, it extends to [xmin, xmax] × [ymin, ymax] × [zmin, zmax].

Properties: The box is not rotated relative to the axes, which makes it inexpensive to compute and test for intersections. Two AABBs intersect if they overlap on all axes; for each axis, the projections must satisfy xmin1 ≤ xmax2 and xmax1 ≥ xmin2 (and similarly for y and z). The volume in 3D is (xmax−xmin)(ymax−ymin)(zmax−zmin).

Computation: Given a set of points or a mesh, the AABB is obtained by taking the component-wise minima and maxima across all points.

Algorithms and usage: AABBs are used in broad-phase collision detection, bounding-volume hierarchies, visibility culling, and as a first step before precise tests. In ray tracing, a slab method computes ray–AABB intersections efficiently. 2D AABBs are common in GUI hit-testing and other planar computations.

Variants and alternatives: AABB contrasts with oriented bounding boxes (OBBs) which allow rotation and can provide a tighter fit. AABBs may be augmented with fattening or used in hierarchical structures like AABB trees.

Limitations: Because they are axis-aligned, AABBs may be loose around rotated or elongated objects, leading to unnecessary tests. They are most effective when objects are not highly rotated relative to the axes.