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  5. VOL 47, NO 3 (2025)
  6. pp. 03-11

Methods of defining geometry of an object in three-dimensional space for polypoint transformations

M.V. Horodetskyi, PhD student, Іu.V. Sydorenko, PhD (Eng. sc.)
National Technical University of Ukraine
«Igor Sikorsky Kyiv Polytechnic Institute»,
Ukraine, 03056, Kyiv, Pr-t Peremohy, 37
E–mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2025, 47(3):03-11

https://doi.org/10.15407/emodel.47.03.003

ABSTRACT

The application of polypoint transformations to modeling the deformation of three-dimensional triangular meshes is considered. Three methods for representing the mesh geometry are proposed and analyzed: the intersection of the planes of a triangle and its normals, orthogonal pla­nes for each vertex, and the intersection of the planes of adjacent triangles. An experimental study was conducted to evaluate the efficiency of each method in modeling two types of nonlinear deformations: twisting around the Z-axis and nonlinear volume expansion.

The accuracy of shape recovery after deformation and the performance of the algorithms were evaluated. The research results showed that the best balance between accuracy and speed is achieved by the method of defining vertices through the intersection of the planes of adjacent triangles. At the same time, its limitations were analyzed, particularly its dependence on the non-parallelism of planes, and the use of the Moore-Penrose pseudoinverse matrix was pro­posed to resolve ambiguities in the transformations.

KEYWORDS

polycoordinate mappings, polypoint transformations, polygonal geometry, transformation basis, transformation object.

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