halfextents

Half extents are a vector describing half the size of a rectangular box along its local axes, measured from the box’s center to each face. If a box has width W, height H, and depth D, the half extents are (W/2, H/2, D/2). The full size of the box is twice the half extents, and the box’s center plus or minus the half extents yields its min and max corners in object or world space, depending on orientation.

In axis-aligned bounding boxes (AABB), the half extents define the box’s extents from its center along the coordinate axes. The minimum corner is center minus the half extents, and the maximum corner is center plus the half extents. For oriented bounding boxes (OBB), the half extents are defined in the box’s local coordinate frame; the box’s orientation determines how those extents map into world space.

Half extents are commonly used to represent collision shapes in 3D engines. They provide a compact description of a box’s dimensions and simplify scaling and transformations: scaling a box by a vector s yields new half extents of (ex*sx, ey*sy, ez*sz). When boxes rotate, the interaction with other geometry is typically handled through established collision tests (for example, using the separating axis theorem) that take into account the rotation and the half extents.

Relation to inertia, if needed, follows standard box formulas: the box’s inertia depends on its mass and its squared extents along the principal axes. Overall, half extents offer a concise, orientation-aware way to specify box size in 3D computations.