Gram matrix of Bernstein basis: properties and applications

DOI10.1016/j.cam.2014.11.037zbMath1309.15048OpenAlexW2012987160MaRDI QIDQ484839

Li-Zheng Lu

Publication date: 8 January 2015

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

Full work available at URL: https://doi.org/10.1016/j.cam.2014.11.037

zbMATH Keywords

approximationGram matrixBernstein basisconstrained dual Bernstein basisfast calculation

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Computer-aided design (modeling of curves and surfaces) (65D17) Direct numerical methods for linear systems and matrix inversion (65F05) Matrices of integers (15B36)

Related Items (6)

Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curves ⋮ On the linear independence of the derivatives of Bernstein polynomials ⋮ Total positivity and accurate computations with Gram matrices of Bernstein bases ⋮ Structured Inversion of the Bernstein Mass Matrix ⋮ Degree reduction of composite Bézier curves ⋮ Explicit \(G^1\) approximation of conic sections using Bézier curves of arbitrary degree

Cites Work

• Unnamed Item
• Bézier representation of the constrained dual Bernstein polynomials
• Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints
• Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
• Optimal multi-degree reduction of Bézier curves with \(G^2\)-continuity
• Construction of dual bases
• Constrained polynomial degree reduction in the \(L_2\)-norm equals best weighted Euclidean approximation of Bézier coefficients
• Explicit \(G^2\)-constrained degree reduction of Bézier curves by quadratic optimization

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