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TitleIntersection points algorithm for piecewise algebraic curves based on Groebner bases.
Author(s) Feng-Gong Lang, Ren-Hong Wang
TypeArticle in Journal
AbstractPiecewise 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 back-substitution process, which makes the algorithm numerically precise. An example is also presented to show the algorithmís feasibility and effectiveness.
KeywordsPiecewise algebraic curve, Multivariate spline, Truncated sign
ISSN1598-5865; 1865-2085/e
URL http://link.springer.com/article/10.1007%2Fs12190-008-0136-2
JournalJ. Appl. Math. Comput.
PublisherSpringer, Berlin/Heidelberg; Korean Society for Computational & Applied Mathematics, Seoul
Translation No
Refereed No