Construction of the Functional Voxel Model for a Spline Curve

Tolok, A. V.; Tolok, N. B.; Sycheva, Anastasiya

doi:10.51130/graphicon-2020-2-3-52

Cited by 3 publications

(1 citation statement)

References 7 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proposed set of approaches for the implementation of means of constructing and calculating analytically presented implicit functions on a given domain allows us to create a new computer computing platform that makes it possible, based on simulated local geometric characteristics, to significantly simplify the representation of complex functions domain to its local analogues (local functions) on a computer and, based on them, to organize complex computational constructions in the form of functional expressions. An example is the FVmodeling of R-functions that allow to obtain set-theoretic operations on the domain of two analytical expression [11,12], etc. Also, the implementation of basic arithmetic procedures allows us to talk about the possibility of using voxel models in solving functional equations, avoiding complex formulations.…”

Section: Discussionmentioning

confidence: 99%

Arithmetic in Functional-Voxel Modeling

Tolok¹,

Tolok²

2022

Self Cite

View full text Add to dashboard Cite

The paper considers the claim that the function-voxel model allows arithmetic operations over the space of values of two different functions given by a single domain. At the same time, there are three possible approaches to solving the problem, leading to a similar result: functional approach -when the analytical representation of functions is involved in the calculations; functional voxel approach -when voxel data representing local geometric characteristics are used in the construction of local functions for further use in the calculation; voxel approach -when exclusively voxel data is used for sequential recalculation of local geometric characteristics of the model. The basic arithmetic operations on functional voxel models are considered, including such procedures as: addition, subtraction, modulo, exponentiation, taking root expressions, multiplication and division of functional voxel models. It is shown that the obtained applicability of arithmetic operations to functional voxel models leads to obtaining new complex functional voxel models.

show abstract

Section: Discussionmentioning

confidence: 99%

Arithmetic in Functional-Voxel Modeling

Tolok¹,

Tolok²

2022

Self Cite

View full text Add to dashboard Cite

show abstract

Functional-Voxel Modelling of Bezie Curves

Sycheva

2022

Geometry &Amp; Graphics

View full text Add to dashboard Cite

The problem of this research is the impossibility of applying parametric functions in theoretical-multiple modeling, that significantly narrows the range of problems solved by analytical models and methods of computational geometry. To expand the possibilities of R-functional modeling application in the field of computer-aided design systems, it is proposed to solve the problem of finding an appropriate representation of parametric curves using functional-voxel computer models. The method of functional-voxel modeling is considered as a computer graphic representation of analytical functions’ areas on the computer. The basic principles and examples of combining R-functional and functional-voxel methods with obtaining R-voxel modeling have been presented. In this case, R-functional operations have been implemented on functional-voxel models by means of functional-voxel arithmetic. Based on the described approach to modeling of theoretical-multiple operations for the function area represented by graphical M-images, two approaches to construction a functional-voxel model of the Bezier curve have been proposed. The first one is based on the sequential construction of the curve’s interior by intersection a positive area of half-planes, which enumeration is performed by De Castiljo algorithm. This approach is limited by the convexity of the curve’s reference polygon. This problem’s solution has been considered. The second approach is based on the application of a two-dimensional function for local zeroing (FLOZ), i.e., a nil segment on the positive area of function values. By consecutive unification of such segments it is proposed to construct the required parametrically given curve. Some features related to operation and realization of the proposed approaches have been described and illustrated in detail. The advantages and disadvantages of described approaches have been highlighted. Assumptions about applicability of proposed algorithms for Bezier curve functional-voxel modeling in solving of various geometric modeling problems have been made.

show abstract

Geometric Aspects of the Functional-Voxel Implementation of the ORCA Algorithm

Tolok

Sycheva

2021

Proceedings of the 31th International Conference on Computer Graphics and Vision. Volume 2

View full text Add to dashboard Cite

The problem of avoiding a collision between moving agents constantly arises in multi-agent systems with decentralized control. The various algorithms for solving this problem are accompanied by computational complexity and increasing computational power requirements as the number of agents in question increases. There are difficulties in adapting these algorithms to practical applications on mobile platforms. It is necessary to develop simpler computational schemes and to apply appropriate models. The most computationally expensive step in the classical collision avoidance algorithm ORCA is to calculate the mutual half-planes of possible collision for each pair of robots and use linear programming to calculate the new velocity from them. The application of the functional-voxel method will simplify the necessary calculations by storing in graphical images the local geometric characteristics of the searched domain. Moreover, the application of such models will make it possible to perform most of the necessary calculations in advance, which will accelerate the work of the algorithm. This paper proposes the construction of a functional-voxel model of a required geometric domain by interpolating the contour of the domain using Bezier curves. The local geometric modelling by means of local zeroing function is used as a tool for functional-voxel curve modelling. The obtained functional-voxel model represents a static case of possible mutual positioning of two agents. A four-dimensional graphical model is proposed to solve the dynamic case. This model performs the distribution of the static case modelling results in the space-time characteristics.

show abstract

Construction of the Functional Voxel Model for a Spline Curve

Cited by 3 publications

References 7 publications

Arithmetic in Functional-Voxel Modeling

Arithmetic in Functional-Voxel Modeling

Functional-Voxel Modelling of Bezie Curves

Geometric Aspects of the Functional-Voxel Implementation of the ORCA Algorithm

Contact Info

Product

Resources

About