Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
A Fast Algorithm for Polygon Containment by Translation (Extended Abstract)
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Polygon Placement Under Translation and Rotation
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
Maximin location of convex objects in a polygon and related dynamic Voronoi diagrams
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
On solving geometric optimization problems using shortest paths
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Extremal polygon containment problems
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Planar geometric location problems and maintaining the width of a planar set
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Intersection detection and separators for simple polygons
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Flip Algorithm for Segment Triangulations
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
A theoretical structure for computational geometry: regions of point-free overlapping circles
ISCGAV'09 Proceedings of the 9th WSEAS international conference on Signal processing, computational geometry and artificial vision
Provably good 2D shape reconstruction from unorganized cross-sections
SGP '08 Proceedings of the Symposium on Geometry Processing
Triangulations of line segment sets in the plane
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
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Given a convex polygon P and an environment consisting of polygonal obstacles, we find the largest similar copy of P that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if P is a convex k-gon and if Q has n corners and edges then we can find the placement of the largest similar copy of P in the environment Q in time &Ogr;(k4n &lgr;4(kn) log n), where &lgr;4 is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of P in time &Ogr;(k2n &lgr;3(kn) log n).