inverseaz

Inverseaz is a term used in some theoretical discussions to denote the inverse operation of a forward azimuth mapping, abbreviated az. In many geometric contexts, az maps a directional vector or a point in space to an azimuth angle relative to a reference plane or axis. Inverseaz, conversely, seeks to recover the original direction or coordinates from the azimuth value, often requiring additional information such as elevation, radius, or a fixed distance.

In practice, inverseaz is typically not unique when the forward az function discards information. If az maps from a full spatial coordinate to an azimuth alone, inverseaz must operate with extra data to produce a single solution. The exact formulation depends on the forward az definition and the chosen reference frame. When additional parameters are supplied, inverseaz can yield a well-defined reconstruction, whereas with insufficient data it results in a set of possible solutions.

Example: in a two-dimensional setting where az maps a point with polar coordinates (r, theta) to the azimuth theta, inverseaz with theta and r can reconstruct Cartesian coordinates as x = r cos theta and y = r sin theta. More generally, inverseaz supports coordinate transformations between polar-like representations and Cartesian form, under appropriate geometric assumptions.

Applications of inverseaz appear in navigation, robotics, computer vision, and geodesy, where recovering spatial direction from an angular measure is needed. See also azimuth, inverse function, and coordinate transformation.