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By Dr. Mark de Berg, Dr. Marc van Kreveld, Prof. Dr. Mark Overmars, Dr. Otfried Cheong Schwarzkopf (auth.)

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Extra resources for Computational Geometry: Algorithms and Applications

Example text

4. 5. 6. 7. 8. (* Now 'lJ is the doubly-connected edge list for O(SI, S2), except that the information about the faces has not been computed yet. *) Determine the boundary cycles in O(SI, S2) by traversing 'lJ. Construct the graph (j whose nodes correspond to boundary cycles and whose arcs connect each hole cycle to the cycle to the left of its leftmost vertex, and compute its connected components. ) for each connected component in (j do Let C be the unique outer boundary cycle in the component and let f denote the face bounded by the cycle.

2. 2 An event point and the changes in the status structure HANDLEEvENTPOINT(p) 1. Let U(p) be the set of segments whose upper endpoint is 2. 3. 4. 5. 6. 7. 8. 9. 26 10. 11. 12. 13. 14. 15. 16. p; these segments are stored with the event point p. ) Find all segments stored in er that contain p; they are adjacent in er. Let L(p) denote the sub set of segments found whose lower endpoint is p, and let C(p) denote the sub set of segments found that contain p in their interior. if L(p) U U (p) U C(p) contains more than one segment then Report pas an interseetion, together with L(p), U(p), and C(p).

We must also store information in the internal nodes to guide the search down the tree to the leaves. At each internal node, we store the segment from the rightmost leaf in its left subtree. (Alternatively, we could store the segments only in interior nodes. This will save some storage. However, it is conceptually simpler to think about the segments in interior nodes as values to guide the search, not as data items. ) Suppose we search in 'T for the segment immediately to the left of some point p which lies on the sweep line.

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