Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Fast Collision Detection Among Multiple Moving Spheres
IEEE Transactions on Visualization and Computer Graphics
Dynamic Compressed Hypertoctrees with Application to the N-Body Problem
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Kinetic Collision Detection for Convex Fat Objects
Algorithmica
Computational Geometry: Theory and Applications
Kinetic convex hulls and delaunay triangulations in the black-box model
Proceedings of the twenty-seventh annual symposium on Computational geometry
Geometric Approximation Algorithms
Geometric Approximation Algorithms
Kinetic 2-centers in the black-box model
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present an efficient method for maintaining a compressed quadtree for a set of moving points in ℝd. Our method works in the black-box KDS model, where we receive the locations of the points at regular time steps and we know a bound dmax on the maximum displacement of any point within one time step. When the number of points within any ball of radius dmax is at most k at any time, then our update algorithm runs in O(nlogk) time. We generalize this result to constant-complexity moving objects in ℝd. The compressed quadtree we maintain has size O(n); under similar conditions as for the case of moving points it can be maintained in O(n logλ) time per time step, where λ is the density of the set of objects. The compressed quadtree can be used to perform broad-phase collision detection for moving objects; it will report in O((λ+k)n) time a superset of all intersecting pairs of objects.