Approximate implicitization of space curves. (English) Zbl 1250.65024

Aigner, Martin; Jüttler, Bert; Poteaux, Adrien

Langer, Ulrich (ed.) et al., Numerical and symbolic scientific computing. Progress and prospects. New York, NY: Springer (ISBN 978-3-7091-0793-5/pbk; 978-3-7091-0794-2/ebook). Texts & Monographs in Symbolic Computation, 1-19 (2012).

Summary: The process of implicitization generates an implicit representation of a curve or surface from a given parametric one. This process is potentially interesting for applications in Computer Aided Design, where the robustness and efficiency of intersection algorithms can be improved by simultaneously considering implicit and parametric representations. This paper gives an brief survey of the existing techniques for approximate implicitization of hyper surfaces. In addition it describes a framework for the approximate implicitization of space curves.
For the entire collection see [Zbl 1234.65014].

MSC:

65D17

Computer-aided design (modeling of curves and surfaces)

Keywords:

graphical examples; implicit representation; Computer Aided Design; intersection algorithm; hyper surfaces; space curves