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Plotting Planar Implicit Curves and Its Applications

  • Jin-San ChengEmail author
  • Junyi Wen
  • Wenjian Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

We present a new method to plot planar implicit curve in a given box \(B \in {\mathbb {R}}^2\). Based on analyzing the geometry of the level sets of the given function, following the points with local maximal (or minimal) curvatures on the level sets, we compute points on each components of the given function in box B and trace each component to plot the curve. We also used this method to find real zeros of bivariate function systems in a given box. The experiments shows that our implementation works well. It works for polynomials with degrees more than 10,000. It also works for non-polynomial case.

Keywords

Plotting Planar implicit curve Level sets Curvature Real solving Bivariate function systems 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Lab of Mathematics Mechanization, Institute of Systems ScienceAcademy of Mathematics and Systems Science, CASBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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