— Due to their panoramic field of view, catadioptric cameras are becoming ubiquitous in many robotics and computer vision applications. Catadioptric cameras with a unique viewpoint are of primary interest, among these is the case where the reflective surface is a parabolic mirror and the camera satisfies the orthographic projection model and which we call paracatadioptric. We here present a new geometrical property (called disparity-circles property) for paracatadioptric cameras and use it to design a video compass algorithm that can compute the 1-axis rotation angle between two views of at least two parallel lines, without any need of internal camera calibration parameters. We present a linear closed form solution suitable for real-time implementation. We then study the performances of our algorithm, its sensitivity to image noise and propose also experimental results with a paracatadioptric camera mounted on a mobile robotic platform.