By C. Berge, D. Ray-Chaudhuri
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Additional resources for Hypergraph Seminar
There is, however, a subtlety regarding this combined approach since, as we will describe next, incremental construction of arrangements requires answering point-location queries. We discuss this issue after presenting various point-location strategies. The Insertion Process Fig. 5. The insertion process of a new curve (dotted) into an existing arrangement of planar curves. The zone of the new curve is lightly shaded and all the newly introduced vertices are marked k) log n), while the incremental construction may take O(n2 ) time.
The traits class exploits the functionality of the parameterized SegmentTraits type to handle the segments that comprise the polyline curves. , Arr segment traits 2
The ﬁrst step consists of choosing a representation for the input data: - We will consider here implicit algebraic curves, and focus more speciﬁcally circles since this corresponds to the current Cgal release. Such a curve is represented by a bivariate polynomial of total degree two. A circular arc is represented by a supporting circle and its two delimiting endpoints, knowing that the arc is oriented counterclockwise. - Two kinds of points—intersection points and endpoints—can be considered in the same way, thus allowing us to have a unique representation.