Bernstein Bézoutians and application to intersection problems

DOI10.1016/j.cagd.2011.08.004zbMath1247.65020OpenAlexW1997494471MaRDI QIDQ426192

Elimane Ba, Mohamed Elkadi

Publication date: 11 June 2012

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2011.08.004

zbMATH Keywords

Bernstein basisBernstein polynomial systemBézoutian matrixsurface-surface intersection

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Uses Software

• mctoolbox

Cites Work

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• Bernstein-Bézoutian matrices
• Intersection and self-intersection of surfaces by means of Bezoutian matrices
• A unified approach to resultant matrices for Bernstein basis polynomials
• Division algorithms for Bernstein polynomials
• Subdivision methods for solving polynomial equations
• Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
• Le formalisme du résultant. (The formalism of resultant)
• Fast QR factorization of Vandermonde matrices
• Explicit factorization of the Vandermonde matrix
• A companion matrix resultant for Bernstein polynomials
• Anisotropic resultant. Complements and applications
• On the stability of transformations between power and Bernstein polynomial forms
• Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basis
• Algorithms for intersecting parametric and algebraic curves I
• Using Algebraic Geometry
• On the optimal stability of the Bernstein basis
• A resultant matrix for scaled Bernstein polynomials

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