A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces

BiBi, Samia; Abbas, Muhammad; Misro, Yushalify; Hu, Gang

doi:10.1109/access.2019.2953496

Cited by 56 publications

(35 citation statements)

References 32 publications

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“…two dimensional 3D three dimensional CAD computer-aided design NURBS non-uniform rational B-spline C 3 parametric continuity of degree three C 5 parametric continuity of degree five CPU central processing unit…”

Section: Dmentioning

confidence: 99%

“…In curve modeling, 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. Schoenberg introduced the trigonometric spline interpolation, spline interpolation of higher derivatives, interpolating spline as limit of polynomials, and Spline interpolation and best quadrature formulae in [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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Section: Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…Hu et al [36,37] proposed a method for constructing generalized developable Bézier and H-Bézier surfaces. Recently, Bibi et al [38] modeled symmetric revolutionary and rotational surfaces using a hybrid trigonometric Bézier surface that was later applied in engineering applications [39].…”

Section: Introductionmentioning

confidence: 99%

Generalized Developable Cubic Trigonometric Bézier Surfaces

et al. 2021

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This paper introduces a new approach for the fabrication of generalized developable cubic trigonometric Bézier (GDCT-Bézier) surfaces with shape parameters to address the fundamental issue of local surface shape adjustment. The GDCT-Bézier surfaces are made by means of GDCT-Bézier-basis-function-based control planes and alter their shape by modifying the shape parameter value. The GDCT-Bézier surfaces are designed by maintaining the classic Bézier surface characteristics when the shape parameters take on different values. In addition, the terms are defined for creating a geodesic interpolating surface for the GDCT-Bézier surface. The conditions appropriate and suitable for G1, Farin–Boehm G2, and G2 Beta continuity in two adjacent GDCT-Bézier surfaces are also created. Finally, a few important aspects of the newly formed surfaces and the influence of the shape parameters are discussed. The modeling example shows that the proposed approach succeeds and can also significantly improve the capability of solving problems in design engineering.

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“…BiBi et al [17,18] suggested a new method for solving the problem of constructing symmetric curves and surfaces by using GHT-Bézier curves with four different shape parameters. e shape of curves can easily be modified by using different values of shape parameters.…”

Section: Introductionmentioning

confidence: 99%

A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

Naseer

Abbas

Emadifar

et al. 2021

Journal of Mathematics

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In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and closed curves are also part of this study.

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A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces

Cited by 56 publications

References 32 publications

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

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

Generalized Developable Cubic Trigonometric Bézier Surfaces

A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

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