atan2ny

atan2ny is a two-argument arctangent function used in mathematics and computing to determine the angle of a two-dimensional vector with components n and y relative to the positive n-axis. The function returns an angle, typically in radians, though some implementations provide degrees as an alternative. The value is usually given in the principal range, such as (-π, π] or (-180°, 180°).

Inputs are the real numbers n and y, representing the horizontal and vertical components of the vector (n, y), respectively. The computed angle is the direction from the positive n-axis to the vector, effectively locating the vector in the plane.

Relation to related functions depends on convention. The standard two-argument arctangent, atan2, is defined as atan2(y, x). If atan2ny is defined as atan2(y, n), then atan2ny(n, y) becomes equivalent to atan2(y, n) with the arguments swapped. If instead atan2ny is defined as atan2(n, y), the resulting angle corresponds to a 90-degree rotation relative to the standard convention. Because conventions vary by library or domain, the precise mapping should be confirmed in the relevant documentation.

Edge cases include when n = 0 and y = 0, where the angle is often undefined or defined by a chosen convention. If n = 0 and y > 0, the angle is typically π/2; if n = 0 and y < 0, it is -π/2. When n > 0, the angle is arctan(y/n) adjusted for the correct quadrant; when n < 0, the result is adjusted by adding or subtracting π as appropriate.

Applications of atan2ny appear in fields such as computer graphics, robotics, navigation, and any domain requiring robust representation of a vector’s direction.