Arctanvertical

Arctanvertical is a nonstandard mathematical concept used to describe the angle between a two-dimensional vector and the vertical axis. The term is not widely adopted in formal mathematics but appears in some contexts such as robotics and computer graphics to emphasize vertical orientation.

In the common informal definition, arctanvertical of a vector with horizontal and vertical components (dx, dy) is defined as arctanvertical(dx, dy) = arctan2(dx, dy), using the two-argument arctangent function. This yields an angle in radians in the range (-pi, pi], representing the rotation from the vertical axis toward the horizontal plane, with positive values indicating tilt toward the positive x direction.

Relation to standard angles: If one uses arctan(y/x) with a single ratio, the result loses quadrant information; arctan2 preserves sign and quadrant. Using arctanvertical thus provides a robust measure of tilt relative to the vertical axis, especially when the vertical component dy is small or zero.

Computation notes: It is robust to dy = 0; in that case, arctan2(dx, 0) returns +/- pi/2 depending on the sign of dx, reflecting a pure horizontal orientation.

Example: For (dx, dy) = (1, 2), arctanvertical = arctan2(1, 2) ≈ 0.4636 radians (26.565 degrees).

Applications and terminology: The label arctanvertical is informal; formal references typically use arctan2 for angles measured from a reference axis with swapped arguments as needed. See also arctan, arctan2, angle of elevation.