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In the past years, research in eye tracking development and applications has attracted much attention and the possibility of interacting with a computer employing just gaze information is becoming more and more feasible. Efforts in eye tracking cover a broad spectrum of fields, system mathematical modeling being an important aspect in this research. Expressions relating to several elements and variables of the gaze tracker would lead to establish geometric relations and to find out symmetrical behaviors of the human eye when looking at a screen. To this end a deep knowledge of projective geometry as well as eye physiology and kinematics are basic. This paper presents a model for a bright-pupil technique tracker fully based on realistic parameters describing the system elements. The system so modeled is superior to that obtained with generic expressions based on linear or quadratic expressions. Moreover, model symmetry knowledge leads to more effective and simpler calibration strategies, resulting in just two calibration points needed to fit the optical axis and only three points to adjust the visual axis. Reducing considerably the time spent by other systems employing more calibration points renders a more attractive model. [ABSTRACT FROM AUTHOR]