ВІЗУАЛІЗАЦІЯ R-ФУНКЦІЙ В ПАРАЛЕЛЬНИХ ОБЧИСЛЮВАЛЬНИХ СИСТЕМАХ ЗІ СПІЛЬНОЮ ПАМ’ЯТТЮ

Authors

  • М. С. Ігнатченко
  • О. В. Кудін

Keywords:

R-ФУНКЦІЯ, ДИСКРЕТНА МОДЕЛЬ, ПАРАЛЕЛЬНИЙ АЛГОРИТМ, ВІЗУАЛІЗАЦІЯ, ОБЧИСЛЮВАЛЬНА СИСТЕМА ЗІ СПІЛЬНОЮ ПАМ’ЯТТЮ

Abstract

The use of numerical methods for solving boundary value problems requires the creation of discrete models of geometric regions of complex shape. The automatic generation of mesh can be divided into two independent problems: creating a formal description of the initial geometric region and building its discrete model based on this description. The most difficult is precisely the first problem. A universal way of formally describing geometric regions of arbitrary shape is to use R-functions, which allow using logical operations of inversion, conjunction, and disjunction over elementary mathematical relations to construct implicit functions that uniquely describe the boundary of an arbitrary geometric object.
This paper proposes a parallel algorithm for constructing and visualizing implicit R-functions in shared-memory computing systems. The algorithm was implemented using the C++ Standard library (C++11 version). The software was implemented and a number of computational experiments were carried out, which showed the effectiveness of the proposed algorithm on computers with various types of processors.

References

1. Choporov S. V., Grebenyuk S. N., Homeniuk S. I. (2016). Functional approach to geometric modeling of technical systems. Zaporizhzhya: ZNU. (in Russian).
2. Choporov S. V., Homeniuk S. I., Alatamneh H. H., Ospischev K. S. (2016). Methods for constructing discrete models: structured and block-structured grids. Visnik Zaporizkogo nacionalnogo universitetu.: Zbirnik naukovih statej. Fiziko-matematichni nauki. Zaporizhzhya: ZNU. Vol. 1. pp. 272–284. (in Russian).
3. Choporov S. V., Lisnyak A. A., Borisovskaya Y. A. , Kozlova O. S., Snezkova L. S. (2016). Discrete Model Building Methods: Unstructured Grids. Visnik Zaporizkogo nacionalnogo universitetu.: Zbirnik naukovih statej. Fiziko-matematichni nauki. Zaporizhzhya: ZNU. Vol. 2. P. 237–250. (in Russian).
4. Rvachev V. L. (1982). Theory of R-functions and Applications. Kyiv: Naukova Dumka. (in Russian).
5. Tolok A. V., Mylcev А. М., Korogod V. L. (2006). Analytical modeling based on graphic transformations in the RANOK system. Visnik Zaporizkogo nacionalnogo universitetu.: Zbirnik naukovih statej. Fiziko-matematichni nauki. Zaporizhzhya: ZNU. Vol. 1. P. 124–133. (in Russian).
6. Tolok A. V. (2016). Functional voxel method in computer simulation. Moscow: FIZMATLIT. (in Russian).
7. Kormen T., Lejzerson Ch., Rivest R., Shtajn K. (2005). Algorithms: construction and analysis. Moscow: Vilyams. (in Russian).
8. William E. L., Harvey E. C. Marching Cubes: A high resolution 3D surface construction algorithm. Computer Graphics. Vol. 21 (4). 1987. P. 163–169.

Published

2020-03-24

Issue

Section

Статті