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@ARTICLE{,
            author = {Blažkov{\'{a}}, Eva and {\v S}{\'{\i}}r, Zbyněk},
          keywords = {algebraic curve, arc-splines, critical points, n ections approximation, support function},
             title = {Identifying and Approximating Monotonous Segments of Algebraic Curves Using Support Function Representation},
           journal = {Computer Aided Geometric Design},
              year = {2014},
          abstract = {Algorithms describing the topology of real algebraic curves search primarily the singular points and they are
usually based on algebraic techniques applied directly to the curve equation. We adopt a dierent approach,
which is primarily based on the identication and approximation of smooth monotonous curve segments,
which can in certain cases cross the singularities of the curve. We use not only the primary algebraic equation
of the planar curve but also (and more importantly) its implicit support function representation. This
representation is also used for an approximation of the segments. This way we obtain an approximate graph
of the entire curve which has several nice properties. It approximates the curve within a given Hausdor
distance. The actual error can be measured eciently and behaves as
O
(
N
3
) where
N
is the number of
segments. The approximate graph is rational and has rational osets. In the simplest case it consists of arc
segments which are eciently represented via the support function. The question of topological equivalence
of the approximate and precise graphs of the curve is also addressed and solved using bounding triangles
and axis projections. The theoretical description of the whole procedure is accompanied by several examples
which show the eciency of our method.},
  Preprint project = {NCMM},
     Preprint year = {2014},
   Preprint number = {10},
       Preprint ID = {NCMM/2014/10}
}