Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Randomized algorithms
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Interval methods for kinetic simulations
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
Journal of Algorithms
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Self-adjusting computation
An experimental analysis of self-adjusting computation
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Whole-program compilation in MLton
Proceedings of the 2006 workshop on ML
A package for exact kinetic data structures and sweepline algorithms
Computational Geometry: Theory and Applications
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Kinetic algorithms via self-adjusting computation
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Kinetic data structures in practice
Kinetic data structures in practice
Imperative self-adjusting computation
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A consistent semantics of self-adjusting computation
ESOP'07 Proceedings of the 16th European conference on Programming
Parallelism in dynamic well-spaced point sets
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Proceedings of the twenty-seventh annual symposium on Computational geometry
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Non-monotonic self-adjusting computation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Dynamic well-spaced point sets
Computational Geometry: Theory and Applications
Asynchronous functional reactive programming for GUIs
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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Kinetic data structures provide a framework for computing combinatorial properties of continuously moving objects. Although kinetic data structures for many problems have been proposed, some difficulties remain in devising and implementing them, especially robustly. One set of difficulties stems from the required update mechanisms used for processing certificate failures--devising efficient update mechanisms can be difficult, especially for sophisticated problems such as those in 3D. Another set of difficulties arises due to the strong assumption in the framework that the update mechanism is invoked with a single event. This assumption requires ordering the events precisely, which is generally expensive. This assumption also makes it difficult to deal with simultaneous events that arise due to degeneracies or due to intrinsic properties of the kinetized algorithms. In this paper, we apply advances on self-adjusting computation to provide a robust motion simulation technique that combines kinetic event-based scheduling and the classic idea of fixed-time sampling. The idea is to divide time into a lattice of fixed-size intervals, and process events at the resolution of an interval. We apply the approach to the problem of kinetic maintenance of convex hulls in 3D, a problem that has been open since 90s. We evaluate the effectiveness of the proposal experimentally. Using the approach, we are able to run simulations consisting of tens of thousands of points robustly and efficiently.