Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

@article{Eppstein1999RaisingRC,
  title={Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions},
  author={David Eppstein and Jeff Erickson},
  journal={Discrete \& Computational Geometry},
  year={1999},
  volume={22},
  pages={569-592}
}
Abstract. The straight skeleton of a polygon is a variant of the medial axis introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an n -gon with r reflex vertices in time O(n1+ε + n8/11+εr9/11+ε) , for any fixed ε >0 , improving the previous best upper bound of O(nr log n) . Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process… 
Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions
TLDR
The straight skeleton of an n -gon with r reflex vertices is constructed in time O(n 1+e + n 8/11+e r 9/11-e ) , for any fixed e >0, improving the previous best upper bound of O(nr log n) .
Computing Mitered Offset Curves Based on Straight Skeletons
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This work extends and adapt Aichholzer and Aurenhammer's triangulation-based straight-skeleton algorithm to make it process real-world data on a conventional finite-precision arithmetic and demonstrates the practical suitability of using straight skeletons for the offsetting of complex PSLGs.
On the Structure of Straight Skeletons
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    ICCSA Workshops
  • 2008
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It is shown that each Mi is a pruned medial axis for a certain convex polygon Qi closely related to G, and an optimal algorithm for computation of all those polygons is given.
On the Structure of Straight Skeletons
  • K. Vyatkina
  • Mathematics, Computer Science
    2008 International Conference on Computational Sciences and Its Applications
  • 2008
TLDR
It is shown that each M-sub i is a pruned medial axis for a certain convex polygon Q<sub>i</sub> closely related to G, and an optimal algorithm for computation of all those polygons is given.
Realistic roofs over a rectilinear polygon
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An algorithm is presented that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n4) preprocessing time.
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This paper shows how to construct a roof over the polygonal footprint of a building that has minimum or maximum volume among all roofs that drain water and extends the standard plane-sweep approach known from the theory of straight skeletons by additional events.
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Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions
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The straight skeleton of an n -gon with r reflex vertices is constructed in time O(n 1+e + n 8/11+e r 9/11-e ) , for any fixed e >0, improving the previous best upper bound of O(nr log n) .
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