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Computer simulation of complex shaped objects is an important problem in dentistry. Microfocal X ray is the most promising approach to construction of comput er models of internal structures [1 7], while 3D scanning is the best approach to implementation of mathematical models of external surfaces. The combination of 3D scan ning with mathematical modeling provides adequate diagnosis. Disadvantages of Monocular Scanning SystemsLaser scanning provides the most accurate approach to 3D mathematical simulation. The minimal set of devices required to implement a laser scanning system includes: camera (C), laser (L), and mechanism for transportation of the object. Different variants of scan ning systems are shown in Fig. 1.Scanning algorithms are based on a triangulation approach to the spatial structure of object taking into account the known geometric parameters and point type camera model. The laser beam is assumed to be indefi nitely thin, which considerably simplifies the mathemati cal apparatus. Let the problem of laser scanning be con sidered for an average monocular scanner (Fig. 2).The process of scanning is reduced to calculation of projection of object R with further positioning in a global frame of references (in this work, we discuss only a local frame of references). Point O of camera and laser calibra tion is suggested to be the origin of the frame of refer ences.Equivalent distance from camera to calibration point is found from the camera angle of vision ( fov) and matrix resolution (MM ′ p ). The resolution of the system is meas ured in pixels:The coefficient for conversion from the pixel based system to the metrical system is:Let us calculate the angle of the central matrix of the camera relative to the central point:The sine theorem gives the required value:The disadvantages of monocular vision scanning systems as tools for constructing object models are discussed. A mathematical model for a laser scanning system based on binocular stereovision is presented. The disadvantages of the system and their effect on model parameters are considered. Fig. 1. Laser scanning systems: a) rotary platform; b) mobile head; c) mobile platform. a b c

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