Intersection points algorithm for piecewise algebraiccurves based on Groebner bases

摘要

Piecewise algebraic curve is defined as the zero set of a bivariate spline. Inthis paper, we mainly study the intersection points algorithm for two given piecewisealgebraic curves based on Groebner bases. Given a domain D and a partition Δ, wepresent a flow and introduce the truncated signs, and then represent the two piecewisealgebraic curves in the global form. We get their Groebner bases with respect to alexicographic order and adopt the interval arithmetic in the back-substitution process,which makes the algorithm numerically precise. An example is also presented toshow the algorithm's feasibility and effectiveness.