A quadratic trigonometric B-Spline as an alternate to cubic B-spline
The idea of the quadratic trigonometric spline (QTS) for the curve modeling approach inspired this paper using a quadratic trigonometric function presented in it. By creating B-spline-like local support basis functions, a competent freeform curve design approach is created. Local support, unity part...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-12-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016822003192 |
| _version_ | 1797978776077860864 |
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| author | Shamaila Samreen Muhammad Sarfraz Abullah Mohamed |
| author_facet | Shamaila Samreen Muhammad Sarfraz Abullah Mohamed |
| author_sort | Shamaila Samreen |
| collection | DOAJ |
| description | The idea of the quadratic trigonometric spline (QTS) for the curve modeling approach inspired this paper using a quadratic trigonometric function presented in it. By creating B-spline-like local support basis functions, a competent freeform curve design approach is created. Local support, unity partition, and positivity are satisfied by the built-in basis functions. These generated local support basis functions give the freeform designed curve technique geometric features like convex hull and variation diminishing. The shape features of point tension, interval tension, and global tension are also observed by employing data point repetitions in a freeform curve scheme. A converted Bernstein Bézier form is used to display the non-uniform freeform curve for consideration in the proposed approach. The recommended method is C2 as a benefit. The proposed method is an addition to the existing family of spline procedures, and it gives a superior quadratic equivalent to the cubic method. |
| first_indexed | 2024-04-11T05:29:29Z |
| format | Article |
| id | doaj.art-9a5afc1f68bc4f148476b3986e59a6ae |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-11T05:29:29Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-9a5afc1f68bc4f148476b3986e59a6ae2022-12-23T04:38:59ZengElsevierAlexandria Engineering Journal1110-01682022-12-0161121143311443A quadratic trigonometric B-Spline as an alternate to cubic B-splineShamaila Samreen0Muhammad Sarfraz1Abullah Mohamed2Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan; Corresponding author.Department of Information Science, College of Computing Sciences & Engineering, Kuwait University, P.O. Box 5969, Safat 13060, KuwaitResearch Centre Future University in Egypt, New Cairo 11835, EgyptThe idea of the quadratic trigonometric spline (QTS) for the curve modeling approach inspired this paper using a quadratic trigonometric function presented in it. By creating B-spline-like local support basis functions, a competent freeform curve design approach is created. Local support, unity partition, and positivity are satisfied by the built-in basis functions. These generated local support basis functions give the freeform designed curve technique geometric features like convex hull and variation diminishing. The shape features of point tension, interval tension, and global tension are also observed by employing data point repetitions in a freeform curve scheme. A converted Bernstein Bézier form is used to display the non-uniform freeform curve for consideration in the proposed approach. The recommended method is C2 as a benefit. The proposed method is an addition to the existing family of spline procedures, and it gives a superior quadratic equivalent to the cubic method.http://www.sciencedirect.com/science/article/pii/S1110016822003192Computational geometryB-splineBernstein-Bézier curveConvex hullVariationDiminishing |
| spellingShingle | Shamaila Samreen Muhammad Sarfraz Abullah Mohamed A quadratic trigonometric B-Spline as an alternate to cubic B-spline Alexandria Engineering Journal Computational geometry B-spline Bernstein-Bézier curve Convex hull Variation Diminishing |
| title | A quadratic trigonometric B-Spline as an alternate to cubic B-spline |
| title_full | A quadratic trigonometric B-Spline as an alternate to cubic B-spline |
| title_fullStr | A quadratic trigonometric B-Spline as an alternate to cubic B-spline |
| title_full_unstemmed | A quadratic trigonometric B-Spline as an alternate to cubic B-spline |
| title_short | A quadratic trigonometric B-Spline as an alternate to cubic B-spline |
| title_sort | quadratic trigonometric b spline as an alternate to cubic b spline |
| topic | Computational geometry B-spline Bernstein-Bézier curve Convex hull Variation Diminishing |
| url | http://www.sciencedirect.com/science/article/pii/S1110016822003192 |
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