Open AccessVARYING THE SHAPE OF A SURFACE WHICH IS DISCRETE PRESENTED BY AN IRREGULAR BALANCED GRID
Author(s) -
Serhii Kovalov,
Svitlana Botvinovska
Publication year - 2021
Publication title -
upravlìnnâ rozvitkom skladnih sistem
Language(s) - English
Resource type - Journals
eISSN - 2412-9933
pISSN - 2219-5300
DOI - 10.32347/2412-9933.2021.45.89-96
Subject(s) - grid , topology (electrical circuits) , node (physics) , coordinate system , affine transformation , computer science , surface (topology) , closure (psychology) , numbering , process (computing) , mathematics , algorithm , geometry , physics , quantum mechanics , combinatorics , economics , market economy , operating system
The article discusses a problem, the solution of which is related to the research previously described in previous publications. This paper demonstrates the solution of the problem of forming a discrete frame, in the form of a balanced irregular grid, discretely represented surface. The described problem is solved by one of the methods of discrete modeling, using the static-geometric method of Professor Kovalev S.N. (SGM). The initial conditions for the formation of such irregular balanced discrete networks are the coordinates of the nodes of the reference loop, the topological organization of the grid and the z-coordinate of one of the internal nodes. Note that irregular grids are characterized by different node and cell topologies. This fact can greatly complicate the modeling process, namely, performing the necessary calculations when calculating the coordinates of discrete grid nodes. To facilitate calculations and simplify numbering of discrete grid nodes, it is proposed to use a topological grid scheme based on a regular grid. For regular grids, each node has a specific number, which greatly facilitates the calculation of node coordinates. The operative change in the shape of the grid can be carried out by connecting the classical coordinate calculations of the discrete SGM grid, that is, by solving the system of equilibrium equations of nodes, with an affine transformation, namely the introduction of the scaling factors of coordinates. The disadvantage of this synthesis of the two methods will be the change in the preassigned reference of contour of the mesh, due to the fact that all coordinates of absolutely all grid nodes are multiplied by the corresponding transformation coefficients. To avoid changing the shape of a given reference contour, it is proposed to use a synthesis of three methods in the work, namely SGM, affine coordinate transformation and a method of functional addition of coordinates. This synthesis of methods will maintain the balance of the discrete grid during the modeling process, and will allow you to simply vary (change) the shape of the simulated surface.