Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Klyachin V. A. Optimization of Calculus Mesh for Cryobiology Problem Based on Multidimensional Hashing Using NumPy. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 355-362. DOI: 10.18500/1816-9791-2014-14-3-355-362, EDN: SMSJZH

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
Full text:
download
(downloads: 150)
Language: 
Russian
Heading: 
Computer Sciences
UDC: 
519.683
DOI: 
10.18500/1816-9791-2014-14-3-355-362
EDN: 
SMSJZH

Optimization of Calculus Mesh for Cryobiology Problem Based on Multidimensional Hashing Using NumPy

Autors: 
Klyachin Vladimir Aleksandrovich, Volgograd State University
Abstract: 

In this paper, by the example of solving the problem of constructing the temperature field in cryotherapy shows efficiency of geometric hashing performed on the basis of the NumPy package for constructing appropriate computational grid. Such an arrangement implies for each node to determine its position relative to the polygonal area of irregular shape. Such forms often modeled surfaces of internal organs. Solution build computational grid will allow for 3D visualization of the temperature field in the vicinity of cryotherapy, which will facilitate the timely temperature control.

Key words: 
cryobiology
computation geometry
geometric hashing
References: 
  1. Cyganov D. I. Processy kriovozdeistviya, apparaty i krio-SVC technologii destrukcii novoobrazovaniy [Processes cryotherapy, apparatus and cryo-microwave technologies of destruction of tumors]. Moscow, RMAPO 2004, 88 p. (in Russian).
  2. Ternovskiy K. S., Gassanov L. G. Nizkie temperatury v medicine [Low temperatures in medicine]. Kiev, Naukova Dumka, 1988, 280 p. (in Russian).
  3. Buzdov B. K. Modelling of cryodestruction of biological tissues. Mat. Model., 2011, vol. 23, no. 3, pp. 27–37 (in Russian).
  4. Alies M. Yu., Kopysov S. P., Novikov A. K. Generation and adaption of finite element mesh for elliptic problem of order two solution. Mat. Model., 1997, vol. 9, no. 2, pp.43–45 (in Russian).
  5. Borovikov S. N., Kryukov I. A., Ivanov I. E. Unstructured triangular mesh generation on curved faces based on Delauney triangulation. Mat. Model., 2005, vol. 17, no. 8, pp. 31–45 (in Russian).
  6. Skvortsov A. V., Mirza N. S.Algoritmy postroeniya i analiza triangulacii [Constructing and Analisys of Triangulation Algorithms]. Tomsk, Tomsk Univ. Press, 2006.
  7. Klyachin V. A., Shirokii A. A. The Delaunay triangulation for multidimensional surfaces and its approximative properties. Rus. Math. [Izv. VUZ. Matematika], 2012, vol. 56, no. 1, pp. 27–34. DOI: 10.3103/S1066 369X12010045.
  8. Klyachin V. A., Pabat E. A. C1-approximation of the level surfaces of functions defined on irregular grids. Sib. Zh. Ind. Mat., 2010, vol. 13, no. 2, pp. 69–78 (in Russian).
  9. Klyachin V. A. On a multidimensional analogue of the Schwarz example. Izv. Math., 2012, vol. 76, no. 4, pp. 681–687. DOI: 10.1070/IM2012v076n04ABEH00 2601.
  10. Preparata F. P., Shamos M. Computational Geometry‘: An Introduction. Berlin ; Heidelberg, Springer-Verlag, 1988.
  11. Berg M., Cheong O., Kreveld M., Overmars M. Computational Geometry. Algorithms and Applications. Berlin ; Heidelberg, Springer-Verlag, 2008.
  12. Wolfson H. J., Rigoutsos I. Geometric Hashing : An Overview. IEEE Computational Science and Engineering, 1997, vol. 4, no. 4, pp. 10–21.
  13. Ling M., Yumin L., Huiqin J., Zhongyong W., Haofei Z. An Improved Method of Geometric Hashing Pattern Recognition. I. J. Modern Education and Computer Science, 2011, no. 3, pp. 1–7.
  14. Mian A. S., Bennamoun M., Owens R. Three-dimensional model-based object recognition and segmentation in cluttered scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, vol. 28, pp. 1584–1601.
  15. NumPy. URL: http://numpy.org/ (Accessed 21, Dec, 2013).
  16. SciPy. URL: http://scipy.org/ (Accessed 21, Dec, 2013).
  17. Newton M. C., Nishino Y., Robinson I. K. BONSU: the interactive phase retrieval suite. Journal of Applied Crystallography, 2012, vol. 45, no. 4, pp. 840–843.
  18. Bryan B. A. High-performance computing tools for the integrated assessment and modelling of social-ecological systems. Environmental Modelling & Software, 2013, vol. 39, pp. 295–303.
  19. Nikolsky D. N. Development of software for the numerical solution of the evolution of the interface of various fluids in porous media complex geological structures using the package NumPy. Uchenye zapiski Orlovskogo gosudarstvennogo universiteta. Ser. Estestvennye, technicheskie i medicinskie nauki, 2012, no. 6–1, pp. 42–47 (in Russian). 
Received: 
06.03.2014
Accepted: 
20.07.2014
Published: 
10.09.2014
  • 880 reads