Elias' Article

Towards and open curved kernel.
Ioannis Z. Emiris, Athanasios Kakargias, Sylvain Pion, Monique Teillaud, and Elias P. Tsigaridas.
In Proc. 20th Annual ACM Symp. Comput. Geom. (SoCG), pp. 438–446, ACM, New York, USA, Jun 8--11 2004.

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Abstract:

Our work goes towards answering the growing need for the robust and efficient manipulation of curved objects in nu- merous applications. The kernel of the cgal library pro- vides several functionalities which are, however, mostly re- stricted to linear objects. We focus here on the arrangement of conic arcs in the plane. Our first contribution is the design, implementation and testing of a kernel for computing arrangements of circu- lar arcs. A preliminary C++ implementation exists also for arbitrary conic curves. We discuss the representation and predicates of the geometric objects. Our implementation is targeted for inclusion in the cgal library. Our second contribution concerns exact and efficient alge- braic algorithms for the case of conics. They treat all inputs, including degeneracies, and they are implemented as part of the library synaps 2.1. Our tools include Sturm sequences, resultants, Descartes' rule, and isolating points. Thirdly, our experiments on circular arcs show that our methods compare favorably to existing alternatives using core 1.6x and leda 4.5.

@inproceedings{ekstt-socg-2004,
  author =       {Ioannis~Z. Emiris and Athanasios Kakargias and
                  Sylvain Pion and Monique Teillaud and
                  Elias~P. Tsigaridas},
  title =        {Towards and open curved kernel},
  booktitle =    SOCG_2004,
  year =         2004,
  pages =        {438--446},
  publisher =    {ACM},
  editor =       {J. Snoeyink and J-D. Boissonnat},
  address =      {New York, USA},
  month =        {Jun 8--11},
  abstract =     "Our work goes towards answering the growing need for
                  the robust and efficient manipulation of curved
                  objects in nu- merous applications. The kernel of
                  the cgal library pro- vides several functionalities
                  which are, however, mostly re- stricted to linear
                  objects.  We focus here on the arrangement of conic
                  arcs in the plane. Our first contribution is the
                  design, implementation and testing of a kernel for
                  computing arrangements of circu- lar arcs. A
                  preliminary C++ implementation exists also for
                  arbitrary conic curves. We discuss the
                  representation and predicates of the geometric
                  objects. Our implementation is targeted for
                  inclusion in the cgal library.  Our second
                  contribution concerns exact and efficient alge-
                  braic algorithms for the case of conics. They treat
                  all inputs, including degeneracies, and they are
                  implemented as part of the library synaps 2.1. Our
                  tools include Sturm sequences, resultants,
                  Descartes' rule, and isolating points.  Thirdly, our
                  experiments on circular arcs show that our methods
                  compare favorably to existing alternatives using
                  core 1.6x and leda 4.5.",
}

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