Computational geometry: an introduction
Computational geometry: an introduction
New results on dynamic planar point location
SIAM Journal on Computing
Applications of a new space-partitioning technique
Discrete & Computational Geometry
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Ray shooting and parametric search
SIAM Journal on Computing
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Ray shooting amidst convex polygons in 2D
Journal of Algorithms
A strong and easily computable separation bound for arithmetic expressions involving square roots
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Straight-skeleton based contour interpolation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Automatically generating large urban environments based on the footprint data of buildings
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Improved Dynamic Planar Point Location
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Motorcycle Graphs and Straight Skeletons
Algorithmica
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Transdichotomous Results in Computational Geometry, I: Point Location in Sublogarithmic Time
SIAM Journal on Computing
Motorcycle graphs: canonical quad mesh partitioning
SGP '08 Proceedings of the Symposium on Geometry Processing
Delaunay triangulations in O(sort(n)) time and more
Journal of the ACM (JACM)
Interactive architectural modeling with procedural extrusions
ACM Transactions on Graphics (TOG)
Theoretical and practical results on straight skeletons of planar straight-line graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Discrete & Computational Geometry - Special Issue: 26th Annual Symposium on Computational Geometry; Guest Editor: David Kirkpatrick
On computing straight skeletons by means of kinetic triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
A faster algorithm for computing motorcycle graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
A faster algorithm for computing motorcycle graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present a new algorithm for computing motorcycle graphs that runs in O(n4/3+ε) time for any ε0, improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with h holes in O(n √(h+1) log2 n + n4/3+ε) expected time. If all input coordinates are O(log n)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with h holes in expected time O(n √{h+1}log3 n). In particular, it means that we can compute the straight skeleton of a simple polygon in O(n log3n) expected time if all input coordinates are O(log n)-bit rationals, while all previously known algorithms have worst-case running time ω(n3/2).