Details:
Title  Intersection points algorithm for piecewise algebraic curves based on Groebner bases.  Author(s)  FengGong Lang, RenHong Wang  Type  Article in Journal  Abstract  Piecewise algebraic curve is defined as the zero set of a bivariate spline. In this paper, we mainly study the intersection points algorithm for two given piecewise algebraic curves based on Groebner bases. Given a domain D and a partition Δ, we present a flow and introduce the truncated signs, and then represent the two piecewise algebraic curves in the global form. We get their Groebner bases with respect to a lexicographic order and adopt the interval arithmetic in the backsubstitution process, which makes the algorithm numerically precise. An example is also presented to show the algorithm’s feasibility and effectiveness.  Keywords  Piecewise algebraic curve, Multivariate spline, Truncated sign  ISSN  15985865; 18652085/e 
URL 
http://link.springer.com/article/10.1007%2Fs1219000801362 
Language  English  Journal  J. Appl. Math. Comput.  Volume  29  Number  12  Pages  357366  Publisher  Springer, Berlin/Heidelberg; Korean Society for Computational & Applied Mathematics, Seoul  Year  2009  Edition  0  Translation 
No  Refereed 
No 
