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Position errors of mechanical parts make great effect on performance of mechanical products. Therefore, it is highly important to accurately measure the position errors and display their error graphs, in order to guarantee and improve the quality of mechanical products. The theory and method of the form and position error evaluation get extensive attention when GB1958-80 was enacted. The evaluation and visualization of the position errors are very difficult.Our country begined to research on it not long ago, but it played an important role in developing our industry and technology.Research on the theory, the mathematical models and other related technologies of the position error evaluation has gotten many achievements in this field,but there are still many problems unsolved, especially in aspects of the theory of the position error projects' visualization, such as position errors, symmetry errors and gradient errors and so on. Because it relates to the mathematical knowledge and computer graphic knowledge, it is concerned by the engineering science and foundation science.This thesis deeply studies the fundamental theory and the mathematical models needed for drawing the position error graphs. On the basis of these studies, the position error visual evaluation system is developed. This thesis studies the fundamental theory of drawing the position error graphs, mainly including selects the 3D wire-frame model to display the position error graphs, deduces out the projective transformation formula of space point, offers the methods of drawing the basic geometrical forms, which include circle, ellipse and cylinder, and deeply discusses the problems of hidden line elimination algorithm. The mathematical models of drawing error graphs are established for position errors, including point position error, axis position error to three datum flats in arbitrary orientation and flat position error, by the least square method and the minimum condition method. The mathematical models of drawing error graphs are established for symmetry errors, including flat symmetry error to datum flat, axis symmetry error to datum flat, flat symmetry error to datum axis and axis symmetry error to datum axis, by the least square method and the minimum condition method. The mathematical models of drawing error graphs are established for gradient errors, including flat gradient error to datum flat, axis gradient error to datum flat in a given orientation and axis gradient error to datum axis in a given orientation, by the least square method and the minimum condition method. On the basis of the theoretical research, the position error visual evaluation system is developed by using Lab Windows/CVI as software platform. The fundamental theory and mathematical models for drawing the position error graphs are proved to be true by simulation. The establishment of software library makes the evaluation and the visualization of the position come