Atan2

atan2 is a two-parameter function for computing the arctangent in the C programming language, C++, Java, PHP, C#, Fortran, MATLAB and many other modern programming languages. The Linux Programmer's Manual [1] says:

"The atan2 C++ function calculates the arctangent of the two variables y and x. It is similar to calculating the arctangent of y/x, except that the signs of both arguments are used to determine the quadrant of the result."

Effectively, this means that atan2(y,x) finds the counterclockwise angle in radians between the x-axis and the vector <x,y> in 2-dimensional Euclidean space, which is useful in many applications involving vectors, such as finding the direction from one point to another.

This is the preferred form [2] for correctly finding the sign of the result in all quadrants. See also inverse trigonometric function.

More specifically, the function atan2(y, x) is defined as the arctangent of y / x with a range from (−π, π], determined by:

• if x = y = 0, then the result is indefinite (the MATLAB atan2 function returns 0),
• if x > 0 and y = 0, then atan2(y, x) = 0,
• if x < 0 and y = 0, then atan2(y, x) = π,
• if y < 0, then −π < atan2(y, x) < 0,
• if y > 0, then 0 < atan2(y, x) < π.

Variations

• In Microsoft Excel, the atan2 function has the two arguments reversed.

External links

• C++ programmer's reference
• MATLAB Function Reference

Other implementations/code for atan2

• http://everything2.com/index.pl?node_id=1008481
• Bearing Between Two Points
• Arctan and Polar Coordinates
• What's 'Arccos'?