On the geometry of parametrized bicubic surfaces

DOI10.1016/j.jsc.2006.02.010zbMath1141.65014OpenAlexW2089283358MaRDI QIDQ2457413

Andre Galligo, Michael Stillman

Publication date: 23 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2006.02.010

zbMATH Keywords

Gröbner basis methodscomputer aided designself-intersectionspline surfacesbicubic Bézier surfacebicubic parametric surface

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (3)

Resultants for unmixed bivariate polynomial systems produced using the Dixon formulation ⋮ Computing intersection and self-intersection loci of parametrized surfaces using regular systems and Gröbner bases ⋮ Intersection and self-intersection of surfaces by means of Bezoutian matrices

Uses Software

• ISOLATE

Cites Work

• Hybrid sparse resultant matrices for bivariate polynomials
• Loop detection in surface patch intersections
• The algebra and geometry of Steiner and other quadratically parametrizable surfaces
• Selfintersection of composite curves and surfaces
• A SURFACE INTERSECTION ALGORITHM BASED ON LOOP DETECTION
• Parametrized surfaces in huge P ³ of bidegree (1,2)
• Selfintersections of a bézier bicubic surface
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