atan2vx

atan2vx is a naming variant for a two-argument arctangent function used to compute the heading of a two-dimensional vector from its x and y components. In practice it is equivalent to the standard atan2 function, typically implemented as θ = atan2(vy, vx), where vy is the vector’s y component and vx its x component. The name emphasizes inputs labeled vx and vy, which can align with velocity components or coordinate axes in programming contexts.

Definition and range: Given real numbers vx and vy, atan2vx returns the angle θ in radians such that the vector (vx, vy) has direction θ relative to the positive x-axis. The function uses the same quadrant rules as atan2, producing values in the interval (-π, π]. The result accounts for the signs of both components to determine the correct quadrant.

Edge cases and interpretation: If both vx and vy are zero, the angle is undefined in pure mathematics; in practice many implementations return zero, NaN, or another sentinel value. When vy is zero, the result is either 0 (vx > 0) or π (vx < 0). When vx is zero, the result is π/2 (vy > 0) or -π/2 (vy < 0). The magnitude of the vector (vx, vy) does not affect the angle; only the direction matters.

Applications and relationship to other functions: atan2vx is commonly used in robotics, computer graphics, navigation, and physics to convert a velocity or displacement vector into an orientation angle. It is essentially the same as atan2, with the naming highlighting the vx/vy component convention. It is related to arctan via the identity atan2(vy, vx) = arctan(vy/vx) adjusted for the proper quadrant when vx ≠ 0.