Modeling of the one-sided surface of the Klein bottle

Ivashchenko Andrey Viktorovich, Stepura Anna Vyacheslavovna

The article discusses two ways of modeling a topological surface - the Klein Bottle in the 3DMax graphics editor. Two variants of the visual image of the surface are presented. Currently, there is a turn in architecture and design towards extraordinary surfaces, the modeling of which presents certain difficulties. The expanding application of information modeling technologies allows for the approximation of complex surfaces with a high degree of accuracy and reliability. Designing and calculating which manually were extremely time-consuming. The observed tendency of the forms of architectural objects to approach biomorphic surfaces, as well as fractal geometry, mark a departure from the prismatic forms of buildings that filled the urban space in the twentieth century. Some paradox inherent in such forms as a Klein Bottle, a Mobius Sheet, the Boy's surface, etc. is at the forefront of modern conceptual solutions in architecture.

Keywords:Klein bottle, one-sided surface, topological surface, information modeling technologies (TIM), 3DMax graphic editor.