The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications

DOI10.1016/j.amc.2010.08.041zbMath1215.65034OpenAlexW2111902845MaRDI QIDQ613232

Li Zhang, Zhiyuan Dong, Jie-qing Tan

Publication date: 20 December 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.08.041

zbMATH Keywords

numerical examplesBézier curveBernstein basisdual basisBall basisBall curveBézier-Said-Wang type generalized Ball basescomputer aided geometric modellinggeneralized Ball basis, Said-Ball curveMardsen identityunifying representationWang-Ball curve

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (1)

Construction of dual \(B\)-spline functions

Uses Software

• CONSURF

Cites Work

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• Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
• Shape preserving properties of the generalised Ball basis
• Dual generalized Bernstein basis
• The weighted dual functionals for the univariate Bernstein basis
• Weighted dual functions for Bernstein basis satisfying boundary constraints
• Dual basis functions for the NS-power basis and their applications
• The dual basis functions for the Bernstein polynomials
• Properties of generalized Ball curves and surfaces
• The dual basis functions for the generalized Ball basis of odd degree
• Unifying representation of Bézier curve and generalized Ball curves
• Dual bases for Wang-Bézier basis and their applications
• Connections between two-variable Bernstein and Jacobi polynomials on the triangle
• A generalized Ball curve and its recursive algorithm

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