Exact and efficient 2D-arrangements of arbitrary algebraic curves

@inproceedings{Eigenwillig2008ExactAE,
  title={Exact and efficient 2D-arrangements of arbitrary algebraic curves},
  author={Arno Eigenwillig and Michael Kerber},
  booktitle={SODA},
  year={2008}
}
We show how to compute the planar arrangement induced by segments of arbitrary algebraic curves with the Bentley-Ottmann sweep-line algorithm. The necessary geometric primitives reduce to cylindrical algebraic decompositions of the plane for one or two curves. We compute them by a new and efficient method that combines adaptive-precision root finding (the Bitstream Descartes method of Eigenwillig et al., 2005) with a small number of symbolic computations, and that delivers the exact result in… CONTINUE READING
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