Inverse problem of cyclographic modeling of spatial curve
The objective of the present study is to justify the possibility of constructive and analytic solution to the inverse problem of cyclographic modeling of a curve of space R3 and development of a respective algorithm. The orthogonal projection and the two components of the cyclographic project...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2022-04-01
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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%202%20(182)%20(%D0%9E%D0%9D%D0%92)/21-27%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C.,%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9B%D1%8E%D0%B1%D1%87%D0%B8%D0%BD%D0%BE%D0%B2%20%D0%95.%20%D0%92..pdf |
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| author | T. M. Myasoedova K. L. Panchuk E. V. Lyubchinov |
| author_facet | T. M. Myasoedova K. L. Panchuk E. V. Lyubchinov |
| author_sort | T. M. Myasoedova |
| collection | DOAJ |
| description | The objective of the present study is to justify the
possibility of constructive and analytic solution to
the inverse problem of cyclographic modeling of a
curve of space R3
and development of a respective
algorithm. The orthogonal projection and the two
components of the cyclographic projection of a spatial
curve form a triad of elements in plane z=0. These
elements are the result of the direct problem solution
and constitute the basis for the inverse problem
solution. The direct problem consists in construction
in plane z=0 of a cyclographic projection (a model)
of a given spatial curve, while the inverse problem
consists in determination of a spatial curve given its
cyclographic projection. Insufficient knowledge on the
inverse problem as well as its relevance in practical
applications, e.g. in cutting tool trajectory calculation
for pocket machining of mechanical engineering
products on NC units, make urgent the definition and
the solution of the inverse problem. In the present
paper a simple convex closed curve is considered as the given cyclographic projection. It is proven that there
exists a unique spatial curve, for which the given curve
constitutes a cyclographic projection. The algorithm
for the inverse problem solution is demonstrated on
examples. |
| format | Article |
| id | doaj-art-5eb27a0d31144f32a8de6a83d6812ec2 |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2022-04-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-5eb27a0d31144f32a8de6a83d6812ec22025-02-02T05:07:02ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412022-04-012 (182)212710.25206/1813-8225-2022-182-21-27Inverse problem of cyclographic modeling of spatial curveT. M. Myasoedova0https://orcid.org/0000-0002-9641-9417K. L. Panchuk1https://orcid.org/0000-0001-9302-8560E. V. Lyubchinov2https://orcid.org/0000-0003-2499-4866Omsk State Technical UniversityOmsk State Technical UniversityOmsk State Technical UniversityThe objective of the present study is to justify the possibility of constructive and analytic solution to the inverse problem of cyclographic modeling of a curve of space R3 and development of a respective algorithm. The orthogonal projection and the two components of the cyclographic projection of a spatial curve form a triad of elements in plane z=0. These elements are the result of the direct problem solution and constitute the basis for the inverse problem solution. The direct problem consists in construction in plane z=0 of a cyclographic projection (a model) of a given spatial curve, while the inverse problem consists in determination of a spatial curve given its cyclographic projection. Insufficient knowledge on the inverse problem as well as its relevance in practical applications, e.g. in cutting tool trajectory calculation for pocket machining of mechanical engineering products on NC units, make urgent the definition and the solution of the inverse problem. In the present paper a simple convex closed curve is considered as the given cyclographic projection. It is proven that there exists a unique spatial curve, for which the given curve constitutes a cyclographic projection. The algorithm for the inverse problem solution is demonstrated on examples. https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%202%20(182)%20(%D0%9E%D0%9D%D0%92)/21-27%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C.,%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9B%D1%8E%D0%B1%D1%87%D0%B8%D0%BD%D0%BE%D0%B2%20%D0%95.%20%D0%92..pdfcyclographic mappingmedial axismedial transformation axisinverse taskα-shellvertex points of the curve |
| spellingShingle | T. M. Myasoedova K. L. Panchuk E. V. Lyubchinov Inverse problem of cyclographic modeling of spatial curve Омский научный вестник cyclographic mapping medial axis medial transformation axis inverse task α-shell vertex points of the curve |
| title | Inverse problem of cyclographic modeling of spatial curve |
| title_full | Inverse problem of cyclographic modeling of spatial curve |
| title_fullStr | Inverse problem of cyclographic modeling of spatial curve |
| title_full_unstemmed | Inverse problem of cyclographic modeling of spatial curve |
| title_short | Inverse problem of cyclographic modeling of spatial curve |
| title_sort | inverse problem of cyclographic modeling of spatial curve |
| topic | cyclographic mapping medial axis medial transformation axis inverse task α-shell vertex points of the curve |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%202%20(182)%20(%D0%9E%D0%9D%D0%92)/21-27%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C.,%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9B%D1%8E%D0%B1%D1%87%D0%B8%D0%BD%D0%BE%D0%B2%20%D0%95.%20%D0%92..pdf |
| work_keys_str_mv | AT tmmyasoedova inverseproblemofcyclographicmodelingofspatialcurve AT klpanchuk inverseproblemofcyclographicmodelingofspatialcurve AT evlyubchinov inverseproblemofcyclographicmodelingofspatialcurve |