Constructive algorithms for forming compound cubic Bezier curves in space and on plane
The article considers two graph-analytical algorithms. The first algorithm makes it possible to form a spatial curve passing through given nodal points with direction vectors specified at these points. The second algorithm allows you to generate a flat compound curve passing through the given n...
| Main Author: | |
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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)/10-16%20%D0%9A%D0%BE%D1%80%D0%BE%D1%82%D0%BA%D0%B8%D0%B9%20%D0%92.%20%D0%90..pdf |
| _version_ | 1826837047552245760 |
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| author | V. A. Korotkii |
| author_facet | V. A. Korotkii |
| author_sort | V. A. Korotkii |
| collection | DOAJ |
| description | The article considers two graph-analytical algorithms.
The first algorithm makes it possible to form a spatial
curve passing through given nodal points with
direction vectors specified at these points. The second
algorithm allows you to generate a flat compound curve
passing through the given nodal points with direction
vectors and curvature radii specified at these points.
The constructed curves are formed by cubic Bezier
segments. Direction vectors are treated as a control for
the shape of the curve being constructed. At the nodal
points, second-order geometric smoothness is ensured,
due to the continuity of the slope and curvature. A
distinctive feature of the proposed algorithms is the
significant use of constructive means of computer
graphics. |
| first_indexed | 2024-04-13T14:18:55Z |
| format | Article |
| id | doaj.art-85339d1cd91d44c0b57c43172a2af741 |
| institution | Directory Open Access Journal |
| issn | 1813-8225 2541-7541 |
| language | English |
| last_indexed | 2025-02-16T11:35:41Z |
| 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-85339d1cd91d44c0b57c43172a2af7412025-02-03T01:08:40ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412022-04-012 (182)101610.25206/1813-8225-2022-182-10-16Constructive algorithms for forming compound cubic Bezier curves in space and on planeV. A. Korotkii0https://orcid.org/0000-0002-5266-4701South Ural State University (National Research University)The article considers two graph-analytical algorithms. The first algorithm makes it possible to form a spatial curve passing through given nodal points with direction vectors specified at these points. The second algorithm allows you to generate a flat compound curve passing through the given nodal points with direction vectors and curvature radii specified at these points. The constructed curves are formed by cubic Bezier segments. Direction vectors are treated as a control for the shape of the curve being constructed. At the nodal points, second-order geometric smoothness is ensured, due to the continuity of the slope and curvature. A distinctive feature of the proposed algorithms is the significant use of constructive means of computer graphics.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)/10-16%20%D0%9A%D0%BE%D1%80%D0%BE%D1%82%D0%BA%D0%B8%D0%B9%20%D0%92.%20%D0%90..pdfcubic segmentdirection vectorcurvaturetorsiongeometric smoothness |
| spellingShingle | V. A. Korotkii Constructive algorithms for forming compound cubic Bezier curves in space and on plane Омский научный вестник cubic segment direction vector curvature torsion geometric smoothness |
| title | Constructive algorithms for forming compound cubic Bezier curves in space and on plane |
| title_full | Constructive algorithms for forming compound cubic Bezier curves in space and on plane |
| title_fullStr | Constructive algorithms for forming compound cubic Bezier curves in space and on plane |
| title_full_unstemmed | Constructive algorithms for forming compound cubic Bezier curves in space and on plane |
| title_short | Constructive algorithms for forming compound cubic Bezier curves in space and on plane |
| title_sort | constructive algorithms for forming compound cubic bezier curves in space and on plane |
| topic | cubic segment direction vector curvature torsion geometric smoothness |
| 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)/10-16%20%D0%9A%D0%BE%D1%80%D0%BE%D1%82%D0%BA%D0%B8%D0%B9%20%D0%92.%20%D0%90..pdf |
| work_keys_str_mv | AT vakorotkii constructivealgorithmsforformingcompoundcubicbeziercurvesinspaceandonplane |