geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

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

coordinate axes A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

of the space. Examples are

axis-aligned rectangle A rectilinear polygon is a polygon all of whose polygon side, 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 def ...

s (or

hyperrectangle In geometry, an orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of intervals. If all of ...

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

Minimum bounding box In geometry, the minimum or smallest bounding or enclosing box for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure a ...

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 pr ...

s, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in

computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

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 may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...

s with principal axes parallel to the coordinate axes.

References

{{reflist Geometry