Abstract
For a planar straight line graph G, its straight skeleton S(G) can be partitioned into two subgraphs S c(G) and S r(G) traced out by the convex and by the reflex vertices of the linear wavefront, respectively. By further splitting S c(G) at the nodes, at which the reflex wavefront vertices vanish, we obtain a set of connected subgraphs M 1, ..., M k of S c(G). We show that each M i is a pruned medial axis for a certain convex polygon Q i closely related to G, and give an optimal algorithm for computation of all those polygons, for 1 ≤ i ≤ k. Here “pruned” means that M i can be obtained from the medial axis M(Q i ) for Q i by appropriately trimming some (if any) edges of M(Q i ) incident to the leaves of the latter.
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Vyatkina, K. (2009). On the Structure of Straight Skeletons. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science VI. Lecture Notes in Computer Science, vol 5730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10649-1_21
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DOI: https://doi.org/10.1007/978-3-642-10649-1_21
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