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Intersection points algorithm for piecewise algebraic curves based on Groebner bases

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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 back-substitution process, which makes the algorithm numerically precise. An example is also presented to show the algorithm’s feasibility and effectiveness.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong, 266071, People’s Republic of China

    Feng-Gong Lang

  2. Institute of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116024, People’s Republic of China

    Ren-Hong Wang

Authors
  1. Feng-Gong Lang
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  2. Ren-Hong Wang
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Correspondence to Feng-Gong Lang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 60533060).

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Lang, FG., Wang, RH. Intersection points algorithm for piecewise algebraic curves based on Groebner bases. J. Appl. Math. Comput. 29, 357–366 (2009). https://doi.org/10.1007/s12190-008-0136-2

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  • DOI: https://doi.org/10.1007/s12190-008-0136-2

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