Bezier curve conjugation for smooth curve joining and corner rounding
The authors propose an analytical method for the smooth connection of two Bezier curves of arbitrary degree using a connecting curve, which is also a Bezier curve. At the points of connection between the connecting curve and the original curves, the smoothness order corresponds to the degrees of...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2025-06-01
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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/2025/%E2%84%962(194)/26-34%20%D0%9A%D1%80%D0%B8%D0%B2%D0%BE%D1%88%D0%B5%D0%B5%D0%B2%20%D0%9E.%20%D0%92.,%20%D0%9C%D0%B0%D0%B2%D1%80%D0%B8%D0%BD%20%D0%A1.%20%D0%92.,%20%D0%A1%D1%82%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%20%D0%90.%20%D0%A1..pdf |
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| Summary: | The authors propose an analytical method for the smooth connection of two Bezier curves of arbitrary
degree using a connecting curve, which is also a Bezier curve. At the points of connection between
the connecting curve and the original curves, the smoothness order corresponds to the degrees of
the original curves. Additional constraints can be imposed on the connecting curve, which frequently
arise when addressing practical design challenges. Theorems establishing the necessary conditions for
the existence of the connecting curve are proven. The capabilities of the proposed method are demonstrated
by solving two problems: the smooth connection of two initially given Bezier curves and the smooth rounding
of an interior corner formed by intersecting initially given Bezier curves. The solution to the second problem
enables both symmetric and asymmetric rounding of corners formed by the intersection of non-straight
lines, while maintaining a high degree of smoothness at the connection points. The influence of additional
constraints on the connecting curve's shape is shown. The proposed mathematical method is based on solving a system of linear equations, where the equations
represent the derivative equality conditions at the connection points and at the points where additional
constraints are applied. Bezier curves are treated as special cases of B-splines. The proposed method is
applicable to both 2D and 3D scenarios. |
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| ISSN: | 1813-8225 2541-7541 |