Computing intersection and self-intersection loci of parametrized surfaces using regular systems and Gröbner bases

DOI10.1016/j.cagd.2011.09.002zbMath1247.65022OpenAlexW1965851114MaRDI QIDQ426175

Dongming Wang, Yan-Li Huang

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.2011.09.002

zbMATH Keywords

algorithmGröbner basesnumerical examplesself-intersectionintersectionminimal varietyparametric locusparametrized surface

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items

Efficient computation of dual space and directional multiplicity of an isolated point ⋮ Symbolic computation of the orthogonal projection of rational curves onto rational parameterized surfaces

Uses Software

• CASA
• Epsilon

Cites Work

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• Computing self-intersection curves of rational ruled surfaces
• Self-intersection detection and elimination in freeform curves and surfaces
• Intersection and self-intersection of surfaces by means of Bezoutian matrices
• A marching method for parametric surface/surface intersection
• Rational algebraic curves. A computer algebra approach
• Elimination methods
• On determining start points for a surface/surface intersection algorithm
• The algebra and geometry of Steiner and other quadratically parametrizable surfaces
• Implicitization of parametric curves and surfaces by using multidimensional Newton formulae
• A new approach to the surface intersection problem
• The intersection of two ruled surfaces.
• Computing triangular systems and regular systems
• The \(\mu \)-basis and implicitization of a rational parametric surface
• Computing the intersection of two ruled surfaces by using a new algebraic approach
• On the geometry of parametrized bicubic surfaces
• Parametrized surfaces in huge P ³ of bidegree (1,2)
• Selfintersections of a bézier bicubic surface