Construction of generalized developable Bézier surfaces with shape parameters

Hu, Gang; Cao, Han; Qin, Xinqiang

doi:10.1002/mma.5242

Cited by 9 publications

(6 citation statements)

References 33 publications

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“…Compared with other curved surfaces, this is also its biggest advantage, so scholars have done a lot of research on developable surfaces. Specifically, there are the structural design of developable surfaces [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], interpolation fitting [17][18][19], mesh approximation [20,21], smooth stitching [22][23][24] and shape optimization [25].…”

Section: Introductionmentioning

confidence: 99%

Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

Lu,

Su,

Zhong

et al. 2023

Mechanics & Industry

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The shape optimization design of the developable surface is an important research topic in CAD/CAM, and it is widely used in engineering manufacturing. In this paper, NSGA-II (the elitist non-dominated sorting genetic algorithm) is used to study the multi-objective shape optimization problem of generalized cubic developable Bézier-like surfaces (GCDBLS, for short) to promote the application of GCDBLS in industrial software and engineering design. Firstly, the shape optimization of developable surfaces is transformed into the shape optimization of dyadic curves based on the point-to-plane duality theory. Secondly, a multi-objective shape parameter optimization model is developed based on three surface optimality criteria (the shortest arc length, the smallest energy, and the smallest curvature change rate of the dual curve). Finally, the results of shape parameter optimization of GCDBLS obtained by NSGA-II are compared with MSSA and MOGOA to verify the feasibility and superiority of NSGA-II in solving multi-objective shape optimization problems for developable surfaces and the flexibility of GCDBLS in the construction of developable surfaces.

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Section: Introductionmentioning

confidence: 99%

Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

Lu,

Su,

Zhong

et al. 2023

Mechanics & Industry

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“…Ammad and Misro [35] constructed a biquintic trigonometric Bézier surface with four shape parameters. 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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“…(a) A developable surface is interpreted as a ruled surface in Euclidean space, and the constraint conditions that the ruled surface should satisfy to achieve accurate developability are derived 2–5 . (b) A developable surface is interpreted as a curve in 3D projective space and is constructed by using the duality between points and planes 6–11 …”

Section: Introductionmentioning

confidence: 99%

Generation of quasi‐developable Q‐Bézier strip via PSO‐based shape parameters optimization

Cao

Zheng

2021

Math Methods in App Sciences

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The generation of quasi‐developable from two boundary curves finds extensive application in manufacturing system. In this paper, we present a new method to generate a quasi‐developable from two Bézier boundary curves via particle swarm optimization (PSO)‐based shape parameters optimization. Owing to the powerful and flexible shape adjustment ability of Q‐Bézier curves, we introduce the multiple shape parameters of Q‐Bézier model into original boundary curves for developability optimization. We formulate the generation of quasi‐developable as a geometric optimization problem in which the objective function is defined as the developability degree of the strip and search within the value range of the shape parameters for the set of optimal shape parameters by PSO to achieve a higher‐accuracy developability. Modeling examples demonstrate that the proposed method is effective, easy to implement, which provides users with the overall shape control of the output strip. With the control points keeping unchanged, the fairness of the surface and its approximation to the original surface can be guaranteed naturally, and the number of optimization variables is greatly reduced compared with previous methods.

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Construction of generalized developable Bézier surfaces with shape parameters

Cited by 9 publications

References 33 publications

Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

Generalized Developable Cubic Trigonometric Bézier Surfaces

Generation of quasi‐developable Q‐Bézier strip via PSO‐based shape parameters optimization

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