Modeling the contour arc based on Dezargues configuration
A new geometric algorithm for modeling the contour arc in the form of a curve of one relationship based on the Dezargues configuration, parameterization of which is performed using the mathematical apparatus "Point Calculus", is proposed. The analysis has shown that the obtained conto...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2022-06-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%203%20(183)%20(%D0%9E%D0%9D%D0%92)/5-9%20%D0%9A%D0%BE%D0%BD%D0%BE%D0%BF%D0%B0%D1%86%D0%BA%D0%B8%D0%B9%20%D0%95.%20%D0%92.,%20%D0%91%D0%B0%D0%BB%D1%8E%D0%B1%D0%B0%20%D0%98.%20%D0%93..pdf |
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| _version_ | 1832569452866043904 |
|---|---|
| author | E. V. Konopatskiy I. G. Balyuba |
| author_facet | E. V. Konopatskiy I. G. Balyuba |
| author_sort | E. V. Konopatskiy |
| collection | DOAJ |
| description | A new geometric algorithm for modeling the contour
arc in the form of a curve of one relationship based
on the Dezargues configuration, parameterization of
which is performed using the mathematical apparatus
"Point Calculus", is proposed. The analysis has shown
that the obtained contour arc has interesting geometric
properties, which can potentially be used for modeling
one-dimensional and multidimensional outlines of high
order smoothness, which constitutes a prospect for
further research. A detailed description of the process of
parametrization the contour arc in the point calculus based
on the proposed geometric algorithm for its construction
with the exception of cumbersome transformations is
presented. The given methods of parametrization of
geometrical objects in the point calculus on the basis of a
simple relation of three points of a straight-line invariant
concerning parallel projection, can be used by other
researchers for the solution of a wide range of problems of
engineering geometry and computer graphics. Examples
of modeling spatial and planar, closed and unclosed arcs
of the circumference, which can find their application as
shape-forming elements of surfaces of technical forms, are
given. |
| format | Article |
| id | doaj-art-4c3c2f4ee0d54c91bee6ce0be6cd69a7 |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-4c3c2f4ee0d54c91bee6ce0be6cd69a72025-02-02T21:15:53ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412022-06-013 (183)5910.25206/1813-8225-2022-183-5-9Modeling the contour arc based on Dezargues configurationE. V. Konopatskiy0https://orcid.org/0000-0003-4798-7458I. G. Balyuba1https://orcid.org/0000-0002-8248-1797Donbas National Academy of Civil Engineering and ArchitectureDonbas National Academy of Civil Engineering and ArchitectureA new geometric algorithm for modeling the contour arc in the form of a curve of one relationship based on the Dezargues configuration, parameterization of which is performed using the mathematical apparatus "Point Calculus", is proposed. The analysis has shown that the obtained contour arc has interesting geometric properties, which can potentially be used for modeling one-dimensional and multidimensional outlines of high order smoothness, which constitutes a prospect for further research. A detailed description of the process of parametrization the contour arc in the point calculus based on the proposed geometric algorithm for its construction with the exception of cumbersome transformations is presented. The given methods of parametrization of geometrical objects in the point calculus on the basis of a simple relation of three points of a straight-line invariant concerning parallel projection, can be used by other researchers for the solution of a wide range of problems of engineering geometry and computer graphics. Examples of modeling spatial and planar, closed and unclosed arcs of the circumference, which can find their application as shape-forming elements of surfaces of technical forms, are given.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%203%20(183)%20(%D0%9E%D0%9D%D0%92)/5-9%20%D0%9A%D0%BE%D0%BD%D0%BE%D0%BF%D0%B0%D1%86%D0%BA%D0%B8%D0%B9%20%D0%95.%20%D0%92.,%20%D0%91%D0%B0%D0%BB%D1%8E%D0%B1%D0%B0%20%D0%98.%20%D0%93..pdfdezargues configurationcontour arcgeometric algorithmpoint calculusorder of smoothnesstangent |
| spellingShingle | E. V. Konopatskiy I. G. Balyuba Modeling the contour arc based on Dezargues configuration Омский научный вестник dezargues configuration contour arc geometric algorithm point calculus order of smoothness tangent |
| title | Modeling the contour arc based on Dezargues configuration |
| title_full | Modeling the contour arc based on Dezargues configuration |
| title_fullStr | Modeling the contour arc based on Dezargues configuration |
| title_full_unstemmed | Modeling the contour arc based on Dezargues configuration |
| title_short | Modeling the contour arc based on Dezargues configuration |
| title_sort | modeling the contour arc based on dezargues configuration |
| topic | dezargues configuration contour arc geometric algorithm point calculus order of smoothness tangent |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%203%20(183)%20(%D0%9E%D0%9D%D0%92)/5-9%20%D0%9A%D0%BE%D0%BD%D0%BE%D0%BF%D0%B0%D1%86%D0%BA%D0%B8%D0%B9%20%D0%95.%20%D0%92.,%20%D0%91%D0%B0%D0%BB%D1%8E%D0%B1%D0%B0%20%D0%98.%20%D0%93..pdf |
| work_keys_str_mv | AT evkonopatskiy modelingthecontourarcbasedondezarguesconfiguration AT igbalyuba modelingthecontourarcbasedondezarguesconfiguration |