Geometric and computer modeling of the main objects for shaping of technical products

Abstract

There is considered geometrical and computer modeling of the main objects for forming products: envelope, enveloping and removable layers based on the joint methodology. There is carried out a study of discriminants of two-dimensional surfaces and three-dimensional hypersurfaces. The obtained results determine the envelope and enveloping families of lines and surfaces from a single viewpoint of analytical and numerical methods, respectively. This methodology is developed for performing 3D modeling by means of CAD, both enveloping and removing layers. There are developed surface models of families of lines after their display in the space. These models are used to analyze the effect on the shape of the envelope of the shape parameters of the forming line, as well as the setting of the product relative to the tool.