Modeling Function Domain for Curves Constructed Based on a Linear Combination of Basis Bernstein Polynomials

Tolok, A. V.; Tolok, N. B.; Локтев, М А

doi:10.1134/s0361768819010079

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…Otherwise, the construction of the curve disrupts because of its' curvature which is peculiar to the parametrical nature. In this case, it's possible to apply the rotation of the coordinate system so that the second anchor point will always lie between the first and the last one [9]. But with an increase of the amount of anchor points the complexity of multiple coordinate system rotations together with their correspondence will arise.…”

Section: Bezier Curvementioning

confidence: 99%

Construction of the Functional Voxel Model for a Spline Curve

Tolok

Sycheva

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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Analytical models are the most accurate method of geometric information representation. Parameterized smooth curves cannot be used in the field of analytical geometry, which explains the necessity for finding of analytical representation of such curves. The article considered the construction of a smooth curve presented in an analytical form and some approaches to finding an analytical model for a parametric Bezier curve. А presentation of a function in the form of its functional areas was chosen as prototype of the analytical model. The selected representation formed on the basis of the De Casteljau's method of constructing the Bezier curve and set-theoretic modeling. The Rvachev functions (R-functions) are used as the mathematical apparatus of set-theoretic operations on function areas. The functional-voxel method makes it possible to simplify the computation of R-functional procedures. An algorithm for constructing the functional area of the Bezier curve is developed on the basis of the presented combined R-voxel approach. The obtained results allow for the conclusions about the adequacy of this approach and its development protentional to construct more complicated structures.

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Section: Bezier Curvementioning

confidence: 99%

Construction of the Functional Voxel Model for a Spline Curve

Tolok

Sycheva

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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“…Figure 7 presents the simulation results of the proposed method and the finite element method, which indicate the similarity of the results of both modeling methods [1,7]. FEM [12,33] FVM Due to the modeling of the application of both point and distributed application of heat to the surface of a complex geometric shape [8][9][10], it is possible to create a full-fledged device for accounting for thermal characteristics during the passage of a cutting tool. At the same time, the construction of complex geometric contours is realized through set-theoretic operations, and specifically, with the R-functional modeling apparatus [2,4,8].…”

Section: Functional-voxel Model Of Thermal Expansionmentioning

confidence: 99%

“…Solving the problem of finding the circumference contour of the processing object, taking into account the influence of differential properties of physical processes, is an urgent task of automated calculations. The method of functional-voxel modeling is one of the possible approaches to the complex solution of this problem [2][3][4][5][6][7][8][9][10], due to the possibility of linking the analytical formulations of physical laws applicable at a given point in a single context of the entire discrete space under consideration. The use of the functional voxel method simplifies the calculations by reducing the calculated expression to a linear polynomial that describes the local functional dependence at a specific point in the simulated space.…”

Section: Introductionmentioning

confidence: 99%

Functional-Voxel Method in Problems of Geometric Modeling of Thermal Characteristics of Objects

Plaksin

Tolok

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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The paper presents an approach developed on the basis of the functional voxel method to the geometric representation of the thermal expansion of objects and temperature stresses in a material when exposed to a surface of a heat source. A discrete geometric law of a single temperature stress in an isotropic heat-conducting body is derived, applicable in the concept of functional voxel modeling. Based on this law, functional-voxel models of thermal stress are developed for a single and distributed application of a heat source. Algorithms of functional-voxel modeling of temperature stress and expansion in the case of distributed thermal loading are presented, which make it possible to construct a loading region of a complex configuration, uniformly form a contour (surface) after material expansion and obtain information about changes in the length (volume) of products. The advantages of the proposed functional-voxel approach to modeling thermal expansion and stress over approaches based on the FEM are substantiated.

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Constructing the Functional Voxel Model for Terrain on the Basis of Bilinear Interpolation of Triangulated Network

Tolok

2020

Advances in Intelligent Systems and Computing

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Modeling Function Domain for Curves Constructed Based on a Linear Combination of Basis Bernstein Polynomials

Cited by 6 publications

References 5 publications

Construction of the Functional Voxel Model for a Spline Curve

Construction of the Functional Voxel Model for a Spline Curve

Functional-Voxel Method in Problems of Geometric Modeling of Thermal Characteristics of Objects

Constructing the Functional Voxel Model for Terrain on the Basis of Bilinear Interpolation of Triangulated Network

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