Azimuthto

Azimuthto is a coined term used in discussions of three-dimensional orientation to describe a descriptor that combines azimuth, the horizontal angle measured from a reference direction, with tilt or elevation to specify a direction in space. The concept does not correspond to a single standardized format, but rather to a family of representations that encode horizontal bearing together with vertical orientation.

Typically, azimuthto is parameterized by two angles: the azimuth α and the tilt β (elevation). A common unit-vector representation derives a direction in 3D space as x = cos β cos α, y = cos β sin α, z = sin β, with α in [0, 2π) and β in [−π/2, π/2]. Some usages encode the same information in a two-component form, such as (cos β cos α, cos β sin α), optionally together with z = sin β. In software and robotics, azimuthto-like representations may be stored as a compact pair of numbers that fully determine the direction.

Origins and usage of the term are informal; azimuthto lacks a universal standard and may be used loosely to denote any combined azimuth-elevation orientation. It appears in discussions of drone control, augmented reality, GIS visualization, and other applications where a direction must be conveyed with a concise two-parameter specification rather than a full three-dimensional rotation.

Etymology and related concepts: the name blends azimuth with a suffix signaling orientation encoding. It is related to azimuth, elevation, bearing, and direction cosines, and to broader representations such as spherical coordinates and quaternions. See also: azimuth, elevation angle, spherical coordinates, unit vectors, orientation representations.