Approximation of planar point sets by point configurations
The paper is devoted to planar linear point sets having hierarchical structure. Point configurations arise naturally in several areas of computational geometry. In the paper, the linear approximation of planar point configurations is discussed. Planar point configuration is considered as a fuzzed...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2023-06-01
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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/2023/%E2%84%962%20(186)%20(%D0%9E%D0%9D%D0%92)/55-59%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
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| _version_ | 1832559171849945088 |
|---|---|
| author | V. Yu. Yurkov |
| author_facet | V. Yu. Yurkov |
| author_sort | V. Yu. Yurkov |
| collection | DOAJ |
| description | The paper is devoted to planar linear point sets having hierarchical structure. Point
configurations arise naturally in several areas of computational geometry. In the
paper, the linear approximation of planar point configurations is discussed. Planar
point configuration is considered as a fuzzed and deformed image of some ideal
configuration. Also, it may be considered as random realizations of ideal one.
Pure images and deformed ones are described by the same hierarchical structures.
The structure of approximating configuration is determined a priory. Image
approximation is realized by mean of least square restoration. The correspondence
of the structures is one of the parameters of approximation. Identification procedure
is realized by linear transformations. Similarity transformations as general ones are
used in the calculations. |
| format | Article |
| id | doaj-art-d099c5d547cd4e10977dcefdcb0d520c |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-d099c5d547cd4e10977dcefdcb0d520c2025-02-03T01:30:42ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412023-06-012 (186)555910.25206/1813-8225-2023-186-55-59Approximation of planar point sets by point configurationsV. Yu. Yurkov0https://orcid.org/0000-0003-2667-8103Omsk State Technical UniversityThe paper is devoted to planar linear point sets having hierarchical structure. Point configurations arise naturally in several areas of computational geometry. In the paper, the linear approximation of planar point configurations is discussed. Planar point configuration is considered as a fuzzed and deformed image of some ideal configuration. Also, it may be considered as random realizations of ideal one. Pure images and deformed ones are described by the same hierarchical structures. The structure of approximating configuration is determined a priory. Image approximation is realized by mean of least square restoration. The correspondence of the structures is one of the parameters of approximation. Identification procedure is realized by linear transformations. Similarity transformations as general ones are used in the calculations. https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%962%20(186)%20(%D0%9E%D0%9D%D0%92)/55-59%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdfpoint setconfigurationapproximationlinear transformationdistance |
| spellingShingle | V. Yu. Yurkov Approximation of planar point sets by point configurations Омский научный вестник point set configuration approximation linear transformation distance |
| title | Approximation of planar point sets by point configurations |
| title_full | Approximation of planar point sets by point configurations |
| title_fullStr | Approximation of planar point sets by point configurations |
| title_full_unstemmed | Approximation of planar point sets by point configurations |
| title_short | Approximation of planar point sets by point configurations |
| title_sort | approximation of planar point sets by point configurations |
| topic | point set configuration approximation linear transformation distance |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%962%20(186)%20(%D0%9E%D0%9D%D0%92)/55-59%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
| work_keys_str_mv | AT vyuyurkov approximationofplanarpointsetsbypointconfigurations |