Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
On the randomized construction of the Delaunay tree
Theoretical Computer Science
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Adaptive set intersections, unions, and differences
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Star-vertices: a compact representation for planar meshes with adjacency information
Journal of Graphics Tools
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth 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
Incremental constructions con BRIO
Proceedings of the nineteenth annual symposium on Computational geometry
SFCGen: A framework for efficient generation of multi-dimensional space-filling curves by recursion
ACM Transactions on Mathematical Software (TOMS)
Streaming computation of Delaunay triangulations
ACM SIGGRAPH 2006 Papers
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
Computational Geometry: Theory and Applications
Parallel geometric algorithms for multi-core computers
Proceedings of the twenty-fifth annual symposium on Computational geometry
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
Reconstructing shapes with guarantees by unions of convex sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Parallel geometric algorithms for multi-core computers
Computational Geometry: Theory and Applications
Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An output-sensitive algorithm for computing projections of resultant polytopes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Delaunay triangulation of non-uniform point distributions by means of multi-grid insertion
Finite Elements in Analysis and Design
Faster geometric algorithms via dynamic determinant computation
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
Computational Geometry: Theory and Applications
A spatial approach to morphological feature extraction from irregularly sampled scalar fields
Proceedings of the Third ACM SIGSPATIAL International Workshop on GeoStreaming
A fast algorithm for well-spaced points and approximate delaunay graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We describe a new implementation of the well-known incremental algorithm for constructing Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons show that our implementation outperforms the best currently available codes for exact convex hulls and Delaunay triangulations, compares very well to the fast non-exact QHull implementation and can be used for quite big input sets in spaces of dimensions up to 6. To circumvent prohibitive memory usage, we also propose a modification of the algorithm that uses and stores only the Delaunay graph (the edges of the full triangulation). We show that a careful implementation of the modified algorithm performs only 6 to 8 times slower than the original algorithm while drastically reducing memory usage in dimension 4 or above.