Approximate Implicitization Using Monoid Curves and Surfaces

Thomas W. Sederberg, Jianmin Zheng, Kris Klimaszewski, Tor Dokken
1999 Graphical Models and Image Processing  
This paper presents an approach to nding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface. High accuracy of the approximation is achieved with a relatively small numberof low-degree curve segments or surface patches. By using monoid curves and surfaces, the method eliminates the undesirable singularities and phantom" branches, normally associated with implicit representation. The monoids are expressed in
more » ... t implicit and parametric equations simultaneously, and upper bounds are derived for the approximate errors of implicitization and inversion equations.
doi:10.1006/gmip.1999.0497 fatcat:zyrvkpv4ine4nfqbgkt53y3n7y