The ultimate planar convex hull algorithm
SIAM Journal on Computing
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Translating a convex polygon to contain a maximum number of points
Computational Geometry: Theory and Applications
Offset-polygon annulus placement problems
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Voronoi Diagrams for Polygon-Offset Distance Functions
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Voronoi Diagrams Based on General Metrics in the Plane
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
Straight Skeletons for General Polygonal Figures in the Plane
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Tentative Prune-And-Search For Computing Fixed-Points With Applications To Geometric Computation
Fundamenta Informaticae
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Aicholzer et al. recently presented a new geometric construct called the straight skeleton of a simple polygon and gave several combinatorial bounds for it. Independently, the current authors defined in companion papers a distance function based on the same offsetting function for convex polygons. In particular, we explored the nearest- and furthest-neighbor Voronoi diagrams of this function and presented algorithms for constructing them. In this paper we give solutions to some constrained annulus placement problems for offset polygons. The goal is to find the smallest annulus region of a polygon containing a set of points. We fix the inner (resp., outer) polygon of the annulus and minimize the annulus region by minimizing the outer offset (resp., maximizing the inner offset). We also solve a a special case of the first problem: finding the smallest translated offset of a polygon containing an entire point set. We extend our results for the standard polygon scaling function as well.