Principles of solid modelling in point calculus

Konopatskiy, E. V.; Бездитный, А. А.; Lagunova, Marina V.; Naidysh, Andrii

doi:10.1088/1742-6596/1901/1/012063

Cited by 13 publications

(9 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It can also be an effective tool for comparing the reference (exact) solution with the numerical solution of partial differential equations by approximating the desired solution by geometric objects with predetermined differential properties [18][19]. Another area of practical application of the proposed method can be a comparison of geometric bodies obtained in point calculus [20].…”

Section: Discussionmentioning

confidence: 99%

An Approach to Comparing Multidimensional Geometric Objects

Seleznev

Konopatskiy

Voronova

et al. 2021

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

View full text Add to dashboard Cite

The paper proposes an approach to the comparison of multidimensional geometric objects, which is used to assess the variational geometric models of multifactor processes and phenomena obtained using the geometric theory of multidimensional interpolation. The proposed approach consists of two stages, the first of which consists in the discretization of multidimensional geometric objects in the form of a set of discretely given points, and the second is in comparing the obtained discrete point sets using a criterion that is essentially similar to the coefficient of determination. In this case, one of the discrete point sets is taken as a reference for comparison with another point set. For a correct comparison of multidimensional geometric models in the form of point equations, which are reduced to a system of parametric equations, it is necessary to perform interconnection of parameters. A computational experiment was carried out on the example of comparing geometric models of the physical and mechanical properties of fine-grained concrete. It showed the possibility of using the proposed approach for comparing multidimensional geometric objects and the reliability of the results obtained in comparison with scientific visualization methods. On the same example, it was found that for an accurate comparison of the investigated geometric models of the physical and mechanical properties of fine-grained concrete, it is enough to discretize 100 points. A further increase in the set of discrete points of the compared geometric objects has no significant effect on the criterion for assessing their similarity.

show abstract

Section: Discussionmentioning

confidence: 99%

An Approach to Comparing Multidimensional Geometric Objects

Seleznev

Konopatskiy

Voronova

et al. 2021

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

View full text Add to dashboard Cite

show abstract

“…-extension of the existing set of built-in commands, in particular, to enable operations on generalized figures (splines), for example, through methods considered in [9,10]; -implementation of the GC language interpreter into a CAD system.…”

Section: Prospects Of the Proposed Methods Includementioning

confidence: 99%

Modeling of geometric correspondences and transformations via geometry constructions language

Boykov

2022

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Geometric correspondences and transformations can be applied in solutions to numerous problems of geometric modeling, mainly in order to create models of curves and surfaces. Among the tools of CAD systems, the geometric transformations are presented in the form of a limited set of editing tools, array tools, tools providing formation of 3D solids and surfaces through motion. In practice, this set of tools restricts application of the wide capabilities of geometric transformations and correspondences. In this regard, it is proposed to model the geometric transformations and correspondences via the geometry construction language. The elements of the geometric transformation theory are analyzed. The geometric transformations are proposed to be created on par with other objects of the geometric model. The commands of the geometry constructions language enabling construction of the transformation objects are considered, their application is discussed. Solutions to practical problems of surface modeling via the geometry constructions language with the use of geometric transformation are demonstrated on examples. The proposed approach allows us to facilitate modeling of curves and surfaces in CAD systems, if said curves and surfaces can be acquired through geometric transformation or correspondence that can be defined via a certain constructive algorithm.

show abstract

“…The work [16] outlined the principles of solid modeling in point calculus and the general concept, which consists in defining a geometric body as a geometric set of points, in which the number of current parameters defining it is equal to the dimension of space. This concept is a consequence of the further development of the geometric theory of multidimensional interpolation [17][18][19][20].…”

Section: Justification Of the Choice Of Point Calculus For The Analytical Description Of Solid Geometric Modelsmentioning

confidence: 99%

“…This concept is a consequence of the further development of the geometric theory of multidimensional interpolation [17][18][19][20]. Based on the proposed concept in [16], examples were given of modeling simple geometric bodies in point calculus, which include a variety of pyramids, prisms, cones and cylinders. In continuation of this work, we will consider other examples of building solid models in point calculus.…”

Section: Justification Of the Choice Of Point Calculus For The Analytical Description Of Solid Geometric Modelsmentioning

confidence: 99%

Solid Modeling of Geometric Objects in Point Calculus

Konopatskiy

Бездитный

2021

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

View full text Add to dashboard Cite

The paper describes an approach to solid modeling of geometric objects in the form of an organized three-parameter set of points in three-dimensional space. The relevance of the research topic is due to the widespread use of solid-state models in various branches of science and technology, mechanical engineering, construction and medicine. Solid-state computer models are currently one of the basic computer graphics tools and an integral part of computer- aided design and calculation systems. It is widely used as one of the control elements of CNC machines and 3D printing, the development of information systems in the design and construction of buildings and structures, finite element calculations of deformed states in aircraft and mechanical engineering, their manufacture in medicine, etc. The choice of point calculus as a mathematical apparatus for the analytical description of solid models of geometric objects is substantiated. Examples of modeling sets of elliptical bodies and toroidal bodies in a simplex of three-dimensional space are given.

show abstract

Principles of solid modelling in point calculus

Cited by 13 publications

References 2 publications

An Approach to Comparing Multidimensional Geometric Objects

An Approach to Comparing Multidimensional Geometric Objects

Modeling of geometric correspondences and transformations via geometry constructions language

Solid Modeling of Geometric Objects in Point Calculus

Contact Info

Product

Resources

About