Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves

DOI10.1016/0167-8396(84)90020-7zbMath0571.65114OpenAlexW2007778702MaRDI QIDQ1061477

David C. Anderson, Thomas W. Sederberg, Ronald N. Goldman

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0167-8396(84)90020-7

zbMATH Keywords

elimination theory computer graphics computational geometry resultant algebraic geometry computer aided geometric design object modeling curve representations

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical approximation and computational geometry (primarily algorithms) (65D99) Graphical methods in numerical analysis (65S05)

Related Items (30)

An application of fast factorization algorithms in computer aided geometric design ⋮ Algebraische Methoden zum Glätten und Schneiden von Splineflächen. (Algebraic methods for smoothing and cutting of spline surfaces) ⋮ Osculating paraboloids of second and third order ⋮ Tracing a planar algebraic curve ⋮ Algorithms for polynomials in Bernstein form ⋮ Realistic computer graphics and free form surfaces ⋮ Computing curve intersection by means of simultaneous iterations ⋮ Parametric cubics as algebraic curves ⋮ The uniqueness of Bézier control points ⋮ Shifting planes always implicitize a surface of revolution ⋮ Bernstein Bézoutians and application to intersection problems ⋮ The Bernstein polynomial basis: a centennial retrospective ⋮ A partial solution to the problem of proper reparametrization for rational surfaces ⋮ The geometric interpretation of inversion formulae for rational plane curves ⋮ Detecting cusps and inflection points in curves ⋮ A hybrid method for computing the intersection and tangency points of plane curves ⋮ A resultant matrix for scaled Bernstein polynomials ⋮ A direct approach to computing the \(\mu\)-basis of planar rational curves ⋮ On the minors of the implicitization Bézout matrix for a rational plane curve ⋮ Using polynomial interpolation for implicitizing algebraic curves ⋮ On the problem of proper reparametrization for rational curves and surfaces ⋮ Exact, efficient, and complete arrangement computation for cubic curves ⋮ A unified approach to resultant matrices for Bernstein basis polynomials ⋮ Some applications of resultants to problems in computational geometry ⋮ Least squares data fitting with implicit functions ⋮ Fast computation of the Bézout and Dixon resultant matrices ⋮ Planar piecewise algebraic curves ⋮ A companion matrix resultant for Bernstein polynomials ⋮ The method of resolvents: A technique for the implicitization, inversion, and intersection of non-planar, parametric, rational cubic curves ⋮ A simple verification of the implicitization formulae for Bézier curves

Cites Work

This page was built for publication: Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves