|
Scientific Visualization
| Issue Year: | 2017 |
| Quarter: | 2 |
| Volume: | 9 |
| Number: | 2 |
| Pages: | 1 - 12 |
|
| Article Name: |
FUNCTIONAL VOXEL METHOD FOR THE COMPUTER CALCULATIONS |
| Authors: |
A.V. Tolok (Russian Federation), N.B. Tolok (Russian Federation) |
| Address: |
A.V. Tolok
a.tolok@stankin.ru
V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russian Federation
N.B. Tolok
nat_tolok@mail.ru
Laboratory of the Computer Graphics, Laboratory of GasHydro-dynamic Tools for Automation, Russian Federation |
| Abstract: |
In this paper, one of the approaches to the voxel visualization tools’ application in the computer representation of algebraic function defined over some field is being considered. Here we offer the thumbnail summary of the functional voxel method intended for the computer solution of a wide class of mathematical problems with geometrical definition. The design principle of the computer model of algebraic function using a set of voxel images is shown. Each image reflects one of the coefficients of the local approximating function, determined for the point environment in the considered field of algebraic function. The final composition of such basic voxel images organizes voxel computer representation for the geometrical model of algebraic function which can be applied in different mathematical computer calculations. As an example, we consider the main computational constructions based on addition/subtraction of algebraic functions, their multiplication/division and taking the modulus. Given examples show the solutions of functional equations with voxel representation of a function as a result. The original geometrical approach to solve the system of algebraic equations using the functional voxel model is considered. Also, the computer calculation of integral characteristics R-functional for the described superposition of algebraic functions is proposed as a tool of square and volume definition for the surfaces and objects of irregular shape. Each example is provided with generalization of the solution for multidimensional space. |
| Language: |
Russian |
|
|
|
