atan2s

atan2s is a term encountered in certain programming and mathematical contexts to denote a two-argument arctangent operation, typically a variant or vectorized form of the standard atan2 function. In practice, atan2s computes the angle θ whose tangent is the quotient of two coordinates, while correctly accounting for the quadrant in which the point lies.

In its common scalar form, atan2s(y, x) returns the angle θ such that tan(θ) = y/x, with θ positioned in the correct quadrant based on the signs of x and y. The output is usually given in radians, within a range such as (−π, π], though some libraries offer an option to return degrees. A key feature of atan2s is its handling of edge cases, including when x is zero or when both arguments are zero (the latter is typically undefined and may raise an exception or return a sentinel value depending on the implementation).

Many environments also implement atan2s as a vectorized or element-wise variant, operating on arrays or lists of coordinate pairs. In this usage, y and x are arrays of equal length, and the function returns a corresponding array of angles, computed independently for each pair. This makes atan2s a convenient tool in fields like robotics, computer graphics, and geographic information systems, where multiple directional angles must be computed efficiently.

Relation to other functions: atan2s is closely related to the single-argument arctangent and to atan2 itself; some libraries simply label the vectorized form as atan2s to emphasize its element-wise behavior. See also atan2, arctan, and angle-detection routines.