Implicitization and distance bounds. (English) Zbl 1124.14049

Aigner, Martin; Szilágyi, Ibolya; Jüttler, Bert; Schicho, Josef

Elkadi, Mohamed (ed.) et al., Algebraic geometry and geometric modeling. Based on the workshop, Nice-Sophia Antipolis, France, September 27–29, 2004. Berlin: Springer (ISBN 3-540-33274-X/hbk). Mathematics and Visualization, 71-85 (2006).

Summary: We address the following problem: given a curve in parametric form, compute the implicit representation of another one that approximates the parametric curve on a certain domain of interest. We study this problem from the numerical point of view: what happens with the output curve if the input curve is slightly changed? It is shown that for any approximate parameterization of the given curve, the curve obtained by an approximate implicitization with a given precision is contained within a certain perturbation region.
For the entire collection see [Zbl 1098.14002].

MSC:

14Q99	Computational aspects in algebraic geometry
13P10	Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)