ArcTan2 / Computation Layer

Calculate the two-argument arctangent (polar angle) from x,y coordinates. Similar to numpy.arctan2() or R's atan2(). Returns angle in radians [-π, π].

Mathematical form: $$\theta =\text{atan2}(y,x)=\{\begin{array}{ll}\text{arctan}(\frac{y}{x})& x>0\\ \text{arctan}(\frac{y}{x})+\pi & x<0,y\ge 0\\ \text{arctan}(\frac{y}{x})-\pi & x<0,y<0\\ \frac{\pi }{2}& x=0,y>0\\ -\frac{\pi }{2}& x=0,y<0\\ \text{undefined}& x=0,y=0\end{array}$$

Common applications:

• Direction calculation (wind direction, vehicle heading)
• Robot navigation (movement angles)
• Computer graphics (rotation angles)
• Signal processing (phase angles)
• Vector analysis (polar coordinates)
• Image processing (gradient direction)

Note: More robust than simple arctan(y/x) as it handles all quadrants correctly.