Abstract
When considering the various areas of computer mathematics, especially geometry sticks out, where the problem analysis clearly and fully illustrates the computer. The discipline called "Computer Geometry" (F.Preparato, M.Sheymos) worthily appreciated by modern scientists. However, the practice of training in the higher education institutions (especially training of future teachers), does not provide studying of the Computer Geometry as an academic subject. Perspectives and methodology of Computer Geometry are developed by detailed study of specific problems, and the selection of the content of such course should be conducted on the basis of certain principles, all of which in total have to reflect the prospects of formation of the identity of the trainee as the subject of education adequately.