By Ageev A.A., Baburin A.E., Gimandi E.K.
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Extra resources for A 3/4-Approximation Algorithm for Multiple Subset Sum
Sample text
So, vi−1 vi blocks the visibility from q to some of the vertices and points currently on the stack. These vertices and points are popped off the stack in Step 4. 5(b)). The vertex vi is now in sorted angular order with the vertices and points on the stack. 5(b)) (which is checked in Step 5a) and therefore, backtracking continues. So, Step 4b is again executed with vi vi+1 as the current forward edge. Observe that two consecutive forward edges may not always be two consecutive edges on bd(vi−1 , vn ).
We summarize the result in the following theorem. 6 Given a point q inside a simple polygon P of n vertices, a subpolygon P1 of P containing both q and the visibility polygon of P from q can be computed in O(n) time such that the boundary of P1 does not wind around q. 3 Computing Visibility of a Point in Polygons with Holes In this section, we present the algorithm of Asano [27] for computing the visibility polygon V (q) from a point q inside a polygon P with h holes with a total of n vertices.
6). 5(b)), backtracking continues with vi vi+1 as the current forward edge. 6). Let m be the intersection point of − →i vi+1 lies to the left of − qv qv −−→ with the polygonal edge containing u. 6(a)). Push m and vi on the stack and vi+1 becomes −−→ the new vi . 6(b)), scan bd(vi+1 , vn ) from vi+1 until a vertex vk is found such that the edge vk−1 vk intersects mvi . Backtracking continues with vk−1 vk as the current forward edge. 7). Let w be the vertex immediately below u on the stack. So, uw is a constructed edge computed earlier by the procedure in Case 2a.