This paper discusses the process of creating a digital twin product, which is virtual model mechanical connection. The modeling was carried out using Pro/ENGINEER software, allows building three-dimensional product assembly process, set electronic models equipment and tools. include mathematical description geometric, physical-mechanical technical parameters objects under consideration. It show...

This paper reports a system for automatic extraction of geometric and non-geometric part information from `engineering drawings' created using computer-aided design and drafting (CADD) tools. A heuristic search is employed to interpret the characteristic attributes of dimension sets that denote linear, diametrical, radial and angular dimensions. Textual callouts are processed using natural lang...

In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor for groups in the category of spaces over a fixed space B. Additionally, we prove that the fiberwise geometric realization functor sends a large class of simpl...

Parametric surface [Fari02] is a surface defined by a tensor-product of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computer-aided geometric design and object modeling aids for many computer graphics applications. Typical examples of such surface include...

When grasping an object using three ngered end-eeectors, a certain geometrical entity can be created based on the grasping points and a deenition of an auxiliary point. This geometric connguration is referred to as the invariant connguration of the three n-gered grasp. This paper exploits the geometric properties of such connguration using screw theory and inner product spaces. The results are ...

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups Fn. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the so...

In this paper, we introduce the fusion product of a generic pair of co-adjoint orbits. This construction provides the geometric dual object to the product in Verlinde fusion algebra. The latter is a quantum deformation of the standard tensor product, the fusion product constructed here is the corresponding deformation of the Cartesian product. Let G be a connected and simply-connected compact s...