Analytical identification of three-dimensional geometric objects by information about the shape of their cross-sections
Keywords:
R-function, spline modeling, visualization, three-dimensional objects.Abstract
In this paper we investigated the possibilities and proposed methods of functional representation of a geometric object in 3D for information on the equation of the boundary sections of the object being restored. The article describes the various methods postreniya geometry equations according to their section. The functional representation of a geometrical object defines it as a unit by one real continuous function of several variables. In 3D on the basis of the theory of R-functions developed by V. L. Rvachev works are devoted to the solution of the inverse problem of analytical geometry. The technique of creation of the equations of the composite geometrical objects described in them is based on operations with the known equations of three-dimensional primitives. At the same time set-theoretic operations are defined in an analytical view with the help of R-functions. However often there is a need of the functional representation of a geometrical object for 3D, being based not on the known equations of three-dimensional primitives, and according to information on the equations of borders of sections of the restored object. Constructed geometric objects using the apparatus of the theory of R-functions and its supporting software. This method of constructing geometric objects is a universal means of modeling and visualization. Analysing method for constructing geometric objects using R-functions, it should be noted that the function is positive inside the body is equal to zero on its surface and it is negative. Using literal parameters significantly expands the design possibilities of the implementation of the simulation geometry. Stored in the computer's memory model allows the researcher using the software three-dimensional interactive computer graphics to manipulate spatial images obtained by varying the value of literal parameters. Construction of mathematical models of geometric objects are their analytic identity, as evidenced by visualization of the derived equations.
References
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Maksimenko-Shejko, K. V, Matsevity, A. M., Tolok, A. V., Shejko, T. I. R-functions and the inverse problem of analytic geometry in three-dimensional space . Inform. technologie. 10, 23-32 (2007).
Rvachev, V. L., Tolok, A. V., Uvarov, R. A., Shejko, T. I. New approaches to the construction of three-dimensional equations of the loci using the R-functions. Vіsn. Zaporіz. University tu. 2, 119 - 130 (2000).
Maksimenko-Shejko, K. V. ., Shejko, T. I. R-function in the mathematical modeling of geometric objects in 3D for the information in 2D. News Zaporіz. the University, 98-104 (2010).
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Copyright (c) 2017 Ю. С. Литвинова, К. В. Максименко-Шейко, Т. И. Шейко
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