A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

Ameer, Moavia; Abbas, Muhammad; Abdeljawad, Thabet; Nazir, Tahir

doi:10.3390/math10030376

Cited by 8 publications

(10 citation statements)

References 28 publications

(36 reference statements)

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“…The B-spline proposal for curves and surfaces was first introduced by Isaac Jacob Schoenberg and developed by Richard Riesenfeld, pioneering its use in CAD and CAM [15][16][17][18]. B-spline curves were developed to solve some of the problems encountered in the Bézier [19]. B-spline generally does not consist of a single segment like Bézier.…”

Section: B-spline Curvesmentioning

confidence: 99%

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Arslan¹,

Gurkahraman²

2023

Computers, Materials &Amp; Continua

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Parametric curves such as Bézier and B-splines, originally developed for the design of automobile bodies, are now also used in image processing and computer vision. For example, reconstructing an object shape in an image, including different translations, scales, and orientations, can be performed using these parametric curves. For this, Bézier and B-spline curves can be generated using a point set that belongs to the outer boundary of the object. The resulting object shape can be used in computer vision fields, such as searching and segmentation methods and training machine learning algorithms. The prerequisite for reconstructing the shape with parametric curves is to obtain sequentially the points in the point set. In this study, a novel algorithm has been developed that sequentially obtains the pixel locations constituting the outer boundary of the object. The proposed algorithm, unlike the methods in the literature, is implemented using a filter containing weights and an outer circle surrounding the object. In a binary format image, the starting point of the tracing is determined using the outer circle, and the next tracing movement and the pixel to be labeled as the boundary point is found by the filter weights. Then, control points that define the curve shape are selected by reducing the number of sequential points. Thus, the Bézier and B-spline curve equations describing the shape are obtained using these points. In addition, different translations, scales, and rotations of the object shape are easily provided by changing the positions of the control points. It has also been shown that the missing part of the object can be completed thanks to the parametric curves.

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Section: B-spline Curvesmentioning

confidence: 99%

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Arslan¹,

Gurkahraman²

2023

Computers, Materials &Amp; Continua

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“…The continuity constraints of surfaces are presented by using the gBS and their applications are also given in this study. This paper’s contribution is the continuity extension of [ 25 , 26 ] carried out by Ameer et al . The following are some of the contributions made by this work:…”

Section: Introductionmentioning

confidence: 99%

Generalized Bézier-like model and its applications to curve and surface modeling

Ameer,

Abbas,

Shafiq

et al. 2024

PLoS ONE

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The subject matter of surfaces in computer aided geometric design (CAGD) is the depiction and design of surfaces in the computer graphics arena. Due to their geometric features, modeling of Bézier curves and surfaces with their shape parameters is the most well-liked topic of research in CAGD/computer-aided manufacturing (CAM). The primary challenges in industries such as automotive, shipbuilding, and aerospace are the design of complex surfaces. In order to address this issue, the continuity constraints between surfaces are utilized to generate complex surfaces. The parametric and geometric continuities are the two metrics commonly used for establishing connections among surfaces. This paper proposes continuity constraints between two generalized Bézier-like surfaces (gBS) with different shape parameters to address the issue of modeling and designing surfaces. Initially, the generalized form of C3 and G3 of generalized Bézier-like curves (gBC) are developed. To check the validity of these constraints, some numerical examples are also analyzed with graphical representations. Furthermore, for a continuous connection among these gBS, the necessary and sufficient G1 and G2 continuity constraints are also developed. It is shown through the use of several geometric designs of gBS that the recommended basis can resolve the shape and position adjustment problems associated with Bézier surfaces more effectively than any other basis. As a result, the proposed scheme not only incorporates all of the geometric features of curve design schemes but also improves upon their faults, which are typically encountered in engineering. Mainly, by changing the values of shape parameters, we can alter the shape of the curve by our choice which is not present in the standard Bézier model. This is the main drawback of traditional Bézier model.

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“…However, trigonometric functions have also received very much attention within geometric modeling. Such as the trigonometric Be´zier curves, [1][2][3][4] the trigonometric B-spline curves, [5][6][7] the trigonometric Hermite curves, 8,9 the trigonometric rational curves, 10,11 etc. The curves constructed in trigonometric function space have been applied in signal analysis, 12 kitchen product design, 13 robot path planning, 14 and other engineering problems.…”

Section: Introductionmentioning

confidence: 99%

A quartic trigonometric interpolatory spline with local free parameters

Liu

2023

Advances in Mechanical Engineering

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The construction of trigonometric interpolatory splines plays a very important role in geometric modeling. This paper presents a quartic trigonometric interpolatory spline with local free parameters. The new spline not only automatically interpolates the given points and achieves C2 continuity, but also owns shape adjustability when the points remain fixed. Some examples show that the shape of the new spline can easily realize local and global adjustment by changing the free parameters.

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A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

Cited by 8 publications

References 28 publications

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Generalized Bézier-like model and its applications to curve and surface modeling

A quartic trigonometric interpolatory spline with local free parameters

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