ANALYTICAL IDENTIFICATION OF THREE-DIMENSIONAL GEOMETRIC OBJECTS ACCORDING TO THE INFORMATION ABOUT THE SHAPE OF THEIR SECTIONS

Authors

Yu. S. Litvinova, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: litjuli56@gmail.com

K. V. Maksymenko-Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail:  m-sh@ipmach.kharkov.ua, ORCID: 0000-0002-7064-2442

T. I. Sheyko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: sheyko@ipmach.kharkov.ua, ORCID: 0000-0003-3295-5998

Abstract

This paper investigates the possibilities and proposes techniques for the functional representation of a geometric object in 3D using information about the equations of the boundaries of the sections of the object being restored. Geometrical objects are constructed using the apparatus of the R-functions theory and a software product supporting it. This method of constructing geometric objects is a universal tool for modeling and visualization. The use of letter parameters significantly expands the design possibilities for the implementation of the modeling of geometric objects. The model stored in the computer’s memory allows a researcher to manipulate the resulting spatial images using the software of interactive three-dimensional computer graphics, varying the values of the literal parameters. The constructed mathematical models of geometric objects are their analytical identification, as evidenced by the visualization of the obtained equations.

Keywords: R-functions, spline, modeling, visualization, three-dimensional objects

References

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Received 26 December 2016

Published 30 March 2017