Unformatted text preview: (= number of edges of the opposing polygon). Show that we can answer the searches for all homein situations using O (log n ) time in total. 2. By adding additional interior points we can transform a balanced pseudotriangulation into a pseudotriangulation where every pseudotriangle has only one concave chain. Since we add at most 6 new pseudotriangles any line intersects at most O (log n ) of these special pseudotriangles. Show how to triangulate the special pseudotriangles using additional points, such that any line intersects at most O (log 2 n ) triangles. Δ (i) (ii) Figure 1: The baysizes of the red chain of Δ in (i) are from left to rigth: 7,3,1,6. Picture (ii) shows how to decompose a pseudotriangle into pseudotriangles with at most one concave chain using additional points. 1...
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 Fall '10
 ErikDemaine
 Polygons, Data Structures, WBBST, concave chain

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