Geometric shapes of C-Bézier curves

Shen, Wanqiang; Wang, Guozhao

doi:10.1016/j.cad.2014.08.007

Cited by 13 publications

(5 citation statements)

References 12 publications

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“…Gang Hu, Li and Xianzhi Hu, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.14, No.4 (2020) In surface modeling, how to construct a developable surface in trigonometric polynomial function space (TPFS, for short) is an interesting problem. During the past 20 years, C-Bézier model defined in TPFS is adopted to design free-form curves and surfaces in CAD/CAM widely (Hoffmann et al, 2006;Shen and Wang, 2015;Yang and Wang, 2004;Zhou et al, 2017). The C-Bézier model retains the excellent properties of the Bézier one, and can be utilized to accurately represent circles and ellipses (Zhang, 1996;Chen et al, 2003).…”

Section: Comparisons With the Previous Workmentioning

confidence: 99%

A novel geometric modeling approach for cubic developable C-Bézier surfaces

2020

JAMDSM

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In this paper, a novel geometric modeling method is proposed to construct generalized cubic developable C-Bézier (GCDC-Bézier, for short) surfaces with shape parameters. By using the control plane with generalized cubic C-Bézier basis function, the GCDC-Bézier surfaces are designed, and the shape of the surfaces are adjusted by changing its shape parameters. In addition, the necessary and sufficient conditions of G 1 continuity and G 2 Beta smooth continuity between two adjacent GCDC-Bézier surfaces are derived. Finally, we also discuss some properties of the GCDC-Bézier surfaces. The approach proposed in this paper provides a valuable alternative to the existing geometric modeling methods of developable surfaces.

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Section: Comparisons With the Previous Workmentioning

confidence: 99%

A novel geometric modeling approach for cubic developable C-Bézier surfaces

2020

JAMDSM

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“…In [31], the quadratic trigonometric spline curve with multiple shape parameters was discussed, where each segment of the spline curve was obtained by four consecutive control points. The necessary and sufficient conditions were derived in [32] for introducing the separate Bézier part in order to represent some regular curves like the cycloid, etc. In [33], the rational Bézier model was generated by mixing polynomial and trigonometric functions.…”

Section: Introductionmentioning

confidence: 99%

Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

et al. 2020

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The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves. The GHT-Bernstein basis functions and Bézier curve with shape parameters are presented. The parametric and geometric continuity constraints for GHT-Bézier curves are constructed. The curvature continuity provides a guarantee of smoothness geometrically between curve segments. Furthermore, we present the curvature junction of complex figures and also compare it with the curvature of the classical Bézier curve and some other applications by using the proposed GHT-Bézier curves. This approach is one of the pivotal parts of construction, which is basically due to the existence of continuity conditions and different shape parameters that permit the curve to change easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve still preserve its characteristics and geometrical configuration. These modeling examples illustrate that our method can be easily performed, and it can also provide us an alternative strong strategy for the modeling of complex figures.

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“…Pei et al [38] replaced the blending function in the second type of Coons patch with a second order trigonometric blending function, a blending function with the shape parameter λ and a RBF-Hermit function to make the patch shape modifiable. Shen and Wang [39] proposed a new transformation algorithm to define the C-Bézier curve with one shape parameter introduced as a seperated form including a Bézier part and a trigonometric part in order to represent some regular curves such as a cycloid or traditional Bézier curve by the C-Bézier curve. Aljure et al [40] found a comparison between the large eddy simulation model and the wall modeled large eddy simulation and a realistic generic car body CAD model according to the styling of the Audi A4 and the BMW 3 series was adopted.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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The modeling of Bézier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem in construction of some engineering symmetric revolutionary curves and symmetric rotation surfaces by using the generalized hybrid trigonometric Bézier (or GHT-Bézier, for short) curve. The shape of the curves and surfaces can be modified by the alteration of shape parameters. The free-form complex curves using GHT-Bézier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bézier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in R 2 and R 3 to show the efficiency of modeling. These symmetric examples show that the proposed method is time saving, effective and efficient in construction of complex engineering symmetric curves and surfaces.

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Geometric shapes of C-Bézier curves

Cited by 13 publications

References 12 publications

A novel geometric modeling approach for cubic developable C-Bézier surfaces

A novel geometric modeling approach for cubic developable C-Bézier surfaces

Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

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

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