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We propose an efficient active camera model to map image coordinates to the camera's pan-tilt orientations in constant time. The model is based on the elliptical locus of the projections of a fixed point on the original image plane of a moving camera. The parametric location of this point along the ellipse defines the change in camera orientation. This model does not require any knowledge of camera parameters other than the focal length. Using synthetic and real data, we show the accuracy of the model by generating seamless spherical panoramas from a set of images and demonstrate the applicability of the model with a real-time active tracking application.