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. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.
Highlights
Splines are a kind of curve, initially evolved in the days prior to computer modeling.Geometric modeling refers to a set of techniques concerned mainly with developing efficient representations of geometric aspects of design
We deal with trigonometric Bézier-like [1,2,3,4,5], Q-Bézier [6], H-Bézier [7], Ball Bézier-like [8], S-λ Bézier-like [9], classical Bézier, B-spline, and NURBS curve, etc
Rational trigonometric B-spline and NURBS are a generalization of B-spline basis
Summary
Splines are a kind of curve, initially evolved in the days prior to computer modeling. The quadratic trigonometric polynomial curve with C1 continuity is introduced by [22] It holds the basic properties of classical B-spline curves. The trigonometric cubic Bézier curve is proposed by [35] with shape parameters. This paper presents new trigonometric cubic B-spline basis functions acquiring shape parameter ξ. To derive new trigonometric B-spline basis functions with shape parameter ξ; To derive trigonometric rational B-spline and NURBS curves; To derive different continuities for basis and curve on uniform and non-uniform knots; To apply the derived curves for 2D and 3D modeling.
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