axisaligned

Axisaligned, typically written axis-aligned, is an adjective used in geometry and computer science to describe objects whose edges or faces are parallel to the coordinate axes. In two dimensions, an axis-aligned rectangle has sides parallel to the x- and y-axes. In three dimensions, an axis-aligned box (AABB) has faces parallel to the x-, y-, and z-planes. The concept extends to higher dimensions as axis-aligned hyperrectangles, defined by intervals aligned with each axis.

Axis-aligned shapes are favored in many applications because their geometry reduces to simple coordinate comparisons. This leads to fast and robust operations, especially intersection tests and containment checks. For example, two axis-aligned boxes in 2D overlap if the maximum of their left coordinates is less than or equal to the minimum of their right coordinates, and the same condition holds for the vertical coordinates. In 3D, a similar test applies across the x, y, and z axes.

Applications span computer graphics, physics simulations, and spatial indexing. Axis-aligned bounding boxes are widely used for broad-phase collision detection, ray tracing, and bounding volumes in physics engines. They also appear in GIS for gridded raster data and in user interface layouts where elements are aligned with screen axes.

Limitations include poor fitting around rotated objects; an axis-aligned box may enclose a rotated object with substantial extra volume. In such cases, oriented bounding boxes or other bounding volumes may provide tighter fits. Related concepts include bounding boxes, hyperrectangles, and oriented bounding boxes.