geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, an axis-aligned object (axis-parallel, axis-oriented) is an object in ''n''-dimensional space whose shape is aligned with the

coordinate axes In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

of the space. Examples are axis-aligned rectangles (or

hyperrectangle In geometry, a hyperrectangle (also called a box, hyperbox, k-cell or orthotopeCoxeter, 1973), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient cond ...

s), the ones with edges parallel to the coordinate axes.

Minimum bounding box In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dime ...

es are often implicitly assumed to be axis-aligned. A more general case is

rectilinear polygon A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is p ...

s, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in computational geometry allow for faster algorithms when restricted to (collections of) axis-oriented objects, such as axis-aligned rectangles or axis-aligned line segments. A different kind of example are axis-aligned ellipsoids, i.e., the

ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathemat ...

s with principal axes parallel to the coordinate axes.

References

{{reflist Geometry