Applications of random sampling to on-line algorithms in computational geometry
Discrete & Computational Geometry
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Journal of the ACM (JACM)
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first 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
A virtual node algorithm for changing mesh topology during simulation
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Robust Kinetic Convex Hulls in 3D
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A cost semantics for self-adjusting computation
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Interactive simulation of surgical needle insertion and steering
ACM SIGGRAPH 2009 papers
CEAL: a C-based language for self-adjusting computation
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Dynamic well-spaced point sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
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In a well-spaced point set the Voronoi cells all have bounded aspect ratio. Well-spaced point sets satisfy some important geometric properties and yield quality Voronoi or simplicial meshes that are important in scientific computations. In this paper, we consider the dynamic well-spaced point set problem, which requires constructing a well-spaced superset of a dynamically changing input set, e.g., as input points are inserted or deleted. We present a dynamic algorithm that allows inserting/deleting points into/from the input in O(log@D) time, where @D is the geometric spread, a natural measure that yields an O(logn) bound when input points are represented by log-size words. We show that this algorithm is time-optimal by proving a lower bound of @W(log@D) for a dynamic update. We also show that this algorithm maintains size-optimal outputs: the well-spaced supersets are within a constant factor of the minimum possible size. The asymptotic bounds in our results work in any constant dimensional space. Experiments with a preliminary implementation indicate that dynamic changes may be performed with considerably greater efficiency than re-constructing a well-spaced point set from scratch. To the best of our knowledge, these are the first time- and size-optimal algorithms for dynamically maintaining well-spaced point sets.