atan2dy

atan2dy is not a standard mathematical term on its own, but in many contexts it is used as a shorthand or documentation label for the two-argument arctangent operation applied to the components dy and dx, that is, the function atan2(dy, dx). This usage mirrors the conventional atan2 function found in many programming languages, and it is typically employed to compute the angle of the vector (dx, dy) relative to the positive x-axis.

Mathematically, atan2(dy, dx) returns an angle theta such that dx = r cos theta and dy = r sin theta for some r >= 0. A key feature of this two-argument form is that it preserves quadrant information and avoids division by zero that occurs with the simpler arctan(dy/dx). The result is usually given in radians, though many libraries can return degrees as well. Commonly, the range of the result is (-pi, pi], while some implementations use [0, 2pi).

Special cases are handled to ensure correct quadrant placement. If dx is zero, the result is pi/2 or -pi/2 depending on the sign of dy. If dy is zero, the result is 0 when dx is positive and pi when dx is negative. If both dx and dy are zero, the angle is undefined in standard mathematics.

Applications of atan2(dy, dx) include computing headings and orientations from velocity components, converting Cartesian coordinates to polar coordinates, and determining object rotation in computer graphics and robotics. The function is distinct from arctan(dy/dx) in that it provides a robust, quadrant-aware angle without requiring an explicit division. See also atan2, arctan2, and vector angle.

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