Geometric approximation scheme for parabolic arcs
A cubic H-Bézier geometric approximation scheme with one free parameter τis introduced for parabolic arcs. It has four control points. The control points are computed by matching the end points and end unit tangents of the two curves and provide two more free parameters. These free parameters are co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447921004214 |
| _version_ | 1828341146757103616 |
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| author | Ayesha Shakeel Maria Hussain Malik Zawwar Hussain |
| author_facet | Ayesha Shakeel Maria Hussain Malik Zawwar Hussain |
| author_sort | Ayesha Shakeel |
| collection | DOAJ |
| description | A cubic H-Bézier geometric approximation scheme with one free parameter τis introduced for parabolic arcs. It has four control points. The control points are computed by matching the end points and end unit tangents of the two curves and provide two more free parameters. These free parameters are computed by curvature continuity constraints. Optimal value of τ is obtained by minimizing the maximum value of the distance between the cubic H-Bézier curve and the concerned parabolic arc. The method is illustrated using different numerical examples which show that the proposed method is economical, reliable and efficient. |
| first_indexed | 2024-04-13T23:08:06Z |
| format | Article |
| id | doaj.art-29689c9b3bf34fa59ed2df179d82e276 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-04-13T23:08:06Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-29689c9b3bf34fa59ed2df179d82e2762022-12-22T02:25:38ZengElsevierAin Shams Engineering Journal2090-44792022-06-01134101643Geometric approximation scheme for parabolic arcsAyesha Shakeel0Maria Hussain1Malik Zawwar Hussain2Department of Mathematics, University of Wah, Wah Cantt, PakistanDepartment of Mathematics, Lahore College for Women University, Lahore, Pakistan; Corresponding authors.Department of Mathematics, University of the Punjab, Lahore, PakistanA cubic H-Bézier geometric approximation scheme with one free parameter τis introduced for parabolic arcs. It has four control points. The control points are computed by matching the end points and end unit tangents of the two curves and provide two more free parameters. These free parameters are computed by curvature continuity constraints. Optimal value of τ is obtained by minimizing the maximum value of the distance between the cubic H-Bézier curve and the concerned parabolic arc. The method is illustrated using different numerical examples which show that the proposed method is economical, reliable and efficient.http://www.sciencedirect.com/science/article/pii/S209044792100421468U0565D0565D0765D18 |
| spellingShingle | Ayesha Shakeel Maria Hussain Malik Zawwar Hussain Geometric approximation scheme for parabolic arcs Ain Shams Engineering Journal 68U05 65D05 65D07 65D18 |
| title | Geometric approximation scheme for parabolic arcs |
| title_full | Geometric approximation scheme for parabolic arcs |
| title_fullStr | Geometric approximation scheme for parabolic arcs |
| title_full_unstemmed | Geometric approximation scheme for parabolic arcs |
| title_short | Geometric approximation scheme for parabolic arcs |
| title_sort | geometric approximation scheme for parabolic arcs |
| topic | 68U05 65D05 65D07 65D18 |
| url | http://www.sciencedirect.com/science/article/pii/S2090447921004214 |
| work_keys_str_mv | AT ayeshashakeel geometricapproximationschemeforparabolicarcs AT mariahussain geometricapproximationschemeforparabolicarcs AT malikzawwarhussain geometricapproximationschemeforparabolicarcs |