3D Models and Algorithms for Computer-Based Parameterization for the Decision of Tasks of Constructive Geometry (at Some Historical Examples)

Abstract

The application of 3D parameterization as a new effective tool for CAD computer graphics editors. The features and capabilities of 3D parameterization to solve geometric problems and carry out their research. Examples of complex and historically known problems: finding the line intersecting the four non-intersecting lines (the problem of transversals), finding the tetrahedron or the Cartesian axes on the basis of their projection in perspective (reconstruction theorem Polke - Schwartz), finding the ball tangent to four given spheres ( Fermat problem), a sophisticated version of the problem of combining conic and quadric. The effectiveness and relevance of the new methods, the necessity of integrating them into the educational process of training students.