Construction of Cubic Trigonometric Curves with an Application of Curve Modelling

Abdul Majeed, Mehwish Naureen, Muhammad Abbas and Kenjiro T. Miura
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Abdul Majeed: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Mehwish Naureen: 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
Kenjiro T. Miura: Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Shizuoka, Japan

Mathematics, 2022, vol. 10, issue 7, 1-22

Abstract: This paper introduces new trigonometric basis functions (TBF) in polynomial and rational form with two shape parameters (SPs). Some classical characteristics, such as the partition of unity, positivity, symmetry, CHP, local control and invariance under affine transformation properties are proven mathematically and graphically. In addition, different continuity conditions at uniform knots (UK) are proven. Some open and closed curves from TBS and trigonometric rational B-spline (TRBS) are generated to test the applicability of the suggested technique, and the influence of the shape parameter is also noted. Furthermore, various objects, such as designing an alphabet, star, butterfly, leaf and 3D cube.

Keywords: trigonometric B-spline basis and curves; rational trigonometric B-spline basis and curves; curve properties; continuity; applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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