# Computational Geometry - Algorithms & Applications by Gregory Levitin, Gregory Levitin

By Gregory Levitin, Gregory Levitin

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Hence. C' is in the same connected component as C, which is not the component of the outer boundary of f. 5 shows that once we have the graph (j. we can create a face record for every component. Then we can set the IncidentFaceO pointers of the half- 37 Chapter 2 LINE SEGMENT INTERSECTION -, f)1\ ~\ J ·\Il~ ! : -00~, I I edges that bound each face I. and we can construct the list InnerComponents(f) and the set OuterComponent(f). How can we construct q? Recall that in the plane sweep algorithm for line segment intersection we always looked for the segments immediately to the left of an event point.

Some implementations of doubly-connected edge lists may also insist that the graph formed by the vertices and edges of the subdivision be connected. This can always be achieved by introducing dummy edges, and has two advantages. Firstly, a simple graph transversal can be used to visit all half-edges, and secondly, the InnerComponentsO list for faces is not necessary. 3 Computing the Overlay of Two Subdivisions Now that we have designed a good representation of a subdivision, we can tackle the general map overlay problem.

They are very valuable, easy to transport, and apparently not so difficult to sell. 1 An art gallery carefully. During the day the attendants can keep a look-out, but at night this has to be done by video cameras. These cameras are usually hung from the ceiling and they rotate about a vertical axis. The images from the cameras are sent to TV screens in the office of the night watch. Because it is easier to keep an eye on few TV screens rather than on many, the number of cameras should be as small as possible.