halfextent

Half extent (often written as half-extents) is a term used in geometry, computer graphics, and physics to describe half the size of a bounding box along each axis. It represents the distance from the box’s center to its faces. For a three-dimensional axis-aligned bounding box with width w, height h, and depth d, the half extents are (w/2, h/2, d/2).

In many systems a box is stored or processed as a center point plus its half extents. From these values, the minimum and maximum corners of the box can be computed as center minus extents and center plus extents. This representation is convenient for many calculations, including collision tests and spatial queries. In two dimensions, the concept is the same for rectangles, where half extents are (width/2, height/2).

Common uses include collision detection in physics engines, ray-box intersections, frustum culling, and bounding volume hierarchies. The half-extents parameter is also referred to as the size of the box in each axis, though it is not the full size itself; the full size equals twice the half extents.

Notes and variations: when boxes are axis-aligned in world space, half extents are straightforward. If a box is rotated, the half extents in world coordinates no longer define a simple AABB; instead, the oriented bounding box or a recalculation of extents in world space is required. In many graphics libraries, the half extents are stored in vectors named extents or halfExtents, and are paired with a center vector to define the box.

See also: bounding box, extents, axis-aligned bounding box, oriented bounding box.