ACTIVE TRANSFORMATION OF PLANES DURING FORMATION OF DISCRETE FRAMES WHITH A STATIC-GEOMETRIC METHOD

Various transformations have found widespread use in applied geometry problems in simulating discrete frameworks of different surfaces with given properties. The paper presents a mathematical apparatus of active coordinate transformation, designed to solve problems of discrete geometric modeling. Under the active transformation of coordinates, the authors propose to consider a clear match between the points of the original and new coordinate systems, while maintaining their numerical correspondence, when the numerical values of the parameters of the original coordinate system will transition to the numerical values of the parameters of the new coordinate system. The paper describes the peculiarities of using active coordinate transformation. In the study is proposes to use the properties of the active plane transformation when switching from The work a rectangular Cartesian coordinate system to a rectangular cylindrical coordinate system for further modeling of discrete frameworks of curved surfaces. The authors of the article focus on that there are many discrete modeling methods among which the generalized static-geometric method of Professor Kovalev S.M. The work demonstrates the possibilities of this method by additional use of active coordinate transformation. It has been proved that the advantages and features of active transformation of coordinates can be used in providing the modeled surface with certain properties necessary for the designer or architect in the process of creating a particular modeled image. Using an active coordinate transformation will simplify the process of forming new geometric shapes of curved surfaces, which are quite difficult to describe analytically. The information presented in the work will be useful for architects and designers in the formation of discrete frames of various surfaces