In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in n-dimensional space whose shape is aligned with the coordinate axes of the space.

Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly assumed to be axis-aligned. A more general case is rectilinear polygons, 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.[1]

A different kind of example are axis-aligned ellipsoids, i.e., the ellipsoids with principal axes parallel to the coordinate axes.

References

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  1. ^ "3D collision detection - Game development | MDN". developer.mozilla.org. 2023-07-07. Retrieved 2023-10-01.

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Minimum bounding box

coordinate for the points in S. Axis-aligned minimal bounding boxes are used as an approximate location of an object in question and as a very simple

Tennis racket theorem

rotation of an object around its first and third principal axes is stable, whereas rotation around its second principal axis (or intermediate axis) is not.

Planet Nine

alignment also switched, from more aligned to anti-aligned with increasing semi-major axis, and from anti-aligned to aligned with increasing perihelion distance

Extreme trans-Neptunian object

trans-Neptunian object (ETNO) orbits are suspected to be aligned with the hypothetical Planet Nine while the blue-colored ETNO orbits are anti-aligned. The highly

Effects of Planet Nine on trans-Neptunian objects

vary with semi-major axis of the object and if the object is in resonance. At smaller semi-major axes the aligned and anti-aligned regions shrink and eventually

Rectilinear polygon

iso-oriented, axis-aligned, and axis-oriented polygons. These adjectives are less confusing when the polygons of this type are rectangles, and the term axis-aligned

Moment of inertia

\end{aligned}}} Here I x x {\displaystyle I_{xx}} denotes the moment of inertia around the x {\displaystyle x} -axis when the objects are rotated

Rotation around a fixed axis

kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational