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This article presents two novel full quadrant approximations for the arctangent function that are specially suitable for real-time applications. The key point of the proposed approximations is that they are valid in a full quadrant. As a result, they can be easily extended to two and four quadrants. The approximations we define are rational functions of second and third order, respectively. This article provides a comparison of the precision and performance of the proposed functions with the best state-of-the-art approximations. Results show that the third-order proposed function outperforms the existing ones in terms of both precision and performance. The second-order proposed function, on the other hand, is the most suitable one for real-time applications, since it has the highest performance. Furthermore, it attains an adequate precision for most applications in the computer vision field.