By Gregory Levitin, Gregory Levitin
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We first deal with the situation around the endpoints of e; later we'll worry about the situation around v. The NextO pointers of the two new half-edges each copy the NextO pointer of the old half-edge that is not its twin. The half-edges to which these pointers point must also update their PrevO pointer and set it to the new halfedges. The correctness of this step can be verified best by looking at a figure. It remains to correct the situation around vertex v. We must set the NextO and PrevO pointers of the four half-edges representing e' and e", and of the four half-edges incident from 52 to v.
These segments partition the horizontal strip [-00: 00] x [0: 1] into n + I regions. Give an O(nlogn) time algorithm to build a binary search tree on the segments in S such that the region containing a query point can be determined in O(log n) time. Also describe the query algorithm in detail. 2 The intersection detection problem for a set S of n line segments is to determine whether there exists a pair of segments in S that intersect. Give a plane sweep algorithm that solves the intersection detection problem in O(nlogn) time.
In applications where the vertices carry no attribute information we could store their coordinates directly in the OriginO field of the edge; there is no strict need for a separate type of vertex record. Even more important is to realize that in many applications the faces of the subdivision carry no interesting meaning (think of the network of rivers or roads that we looked at before). If that is the case, we can completely forget about the face records, and the IncidentFaceO field of half-edges.
Computational Geometry - Algorithms & Applications by Gregory Levitin, Gregory Levitin