On the numerical condition of algebraic curves and surfaces 1. Implicit equations
Computer Aided Geometric Design
Computer Aided Geometric Design
Parametrization of cubic algebraic surfaces
Proceedings on Mathematics of surfaces II
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Algorithms for intersecting parametric and algebraic curves II: multiple intersections
Graphical Models and Image Processing
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Stabilization of polynomial systems solving with Groebner bases
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Rational parametrization of surfaces
Journal of Symbolic Computation
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Univariate polynomials: nearly optimal algorithms for factorization and rootfinding
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Symbolic and numeric methods for exploiting structure in constructing resultant matrices
Journal of Symbolic Computation
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Mathematical Methods for Curves and Surfaces
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Parametrization of approximate algebraic curves by lines
Theoretical Computer Science - Algebraic and numerical algorithm
Distance bounds of ε-points on hypersurfaces
Theoretical Computer Science
ACM Communications in Computer Algebra
Parametrization of ε-rational curves: extended abstract
Proceedings of the 2009 conference on Symbolic numeric computation
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In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ε-irreducible algebraic surfaces of degree d having an ε-singularity of multiplicity d - 1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance ε 0 and an ε-irreducible algebraic surface V of degree d, the algorithm computes a new algebraic surface V-, that is rational, as well as a rational parametrization of V-. In addition, in the error analysis we show that the output surface V- and the input surface V are close. More precisely, we prove that V- lies in the offset region of V at distance, at most, O(ε1/(2d)).