Piecewise approximate implicitization: experiments using industrial data. (English) Zbl 1107.65307

Shalaby, Mohamed F.; Thomassen, Jan B.; Wurm, Elmar M.; Dokken, Tor; Jüttler, Bert

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, 17-51 (2006).

Summary: We compare several methods for approximate implicitization by piecewise polynomials which have been developed by the authors, and a linear-algebra-based numerical method for implicitication which is provided as a part of MAPLE. We investigate both quantitative criteria (such as computing time, memory use, and the error of the approximation) and qualitative criteria. As a demonstrated by the results, piecewise approximate implicitization is able to handle surfaces arising in industrial applications. However, special care has to be taken to avoid additional branches and unwanted singularities.
For the entire collection see [Zbl 1098.14002].

MSC:

65D17

Computer-aided design (modeling of curves and surfaces)

Keywords:

graphical examples; parametric representations; NURBS surface CAD; approximate implicitization; surfaces

Software:

Maple