Full quadrant approximations for the arctangent function

Two novel full quadrant approximations for the arctangent function that are specially suitable for real-time applications are studied. The key point of the proposed approximations is that they can be easily extended to two and four quadrants. Results show that the third-order proposed function outperforms the existing ones in terms of both precision and performance. Specifically, it is about 15% more accurate and about 1.5 times faster than the best existing one. On the other hand, the second-order proposed function is the most suitable for realtime applications: it is 2.6 and three times faster than the best existing one in the two- and four-quadrant approximations, respectively. Furthermore, it has a precision of about 0.18°, which is adequate for most applications in the computer vision field.