Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Abdul Majeed, Muhammad Abbas, Faiza Qayyum, Kenjiro T. Miura, Md Yushalify Misro and Tahir Nazir
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Abdul Majeed: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Faiza Qayyum: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Kenjiro T. Miura: Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8011, Japan
Md Yushalify Misro: School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
Tahir Nazir: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Mathematics, 2020, vol. 8, issue 12, 1-25

Abstract: Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ ∈ [ 0 , 4 ] . All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C 3 and C 5 continuities for trigonometric B-spline basis and C 3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2 D and 3 D models are also constructed using proposed curves.

Keywords: cubic trigonometric b-spline functions; cubic curves and its properties; C 3 and C 5 continuity; geometric modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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