Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Delaunay based shape reconstruction from large data
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
The probabilistic complexity of the Voronoi diagram of points on a polyhedron
Proceedings of the eighteenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes
Computational Geometry: Theory and Applications
Provably good surface sampling and approximation
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Learning smooth objects by probing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Provable dimension detection using principal component analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Delaunay triangulations approximate anchor hulls
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
The implicit structure of ridges of a smooth parametric surface
Computer Aided Geometric Design
Journal of Computer and System Sciences
Delaunay triangulations approximate anchor hulls
Computational Geometry: Theory and Applications
Learning smooth shapes by probing
Computational Geometry: Theory and Applications
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Complexity of Delaunay triangulation for points on lower-dimensional polyhedra
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Provably correct reconstruction of surfaces from sparse noisy samples
Pattern Recognition
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
The implicit structure of ridges of a smooth parametric surface
Computer Aided Geometric Design
High-quality consistent meshing of multi-label datasets
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
SMI 2011: Full Paper: Localized Cocone surface reconstruction
Computers and Graphics
Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Contour-Based terrain model reconstruction using distance information
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Efficient large-scale terrain rendering method for real-world game simulation
Edutainment'06 Proceedings of the First international conference on Technologies for E-Learning and Digital Entertainment
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
Computational Geometry: Theory and Applications
Complexity analysis of random geometric structures made simpler
Proceedings of the twenty-ninth annual symposium on Computational geometry
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
RDELA--a Delaunay-triangulation-based, location and covariance estimator with high breakdown point
Statistics and Computing
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It is well known that the complexity of the Delaunay triangulation of N points in R 3, i.e. the number of its faces, can be O (N2). The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay triangulation of a set of points measured on a surface.In this paper, we bound the complexity of the Delaunay triangulation of points distributed on generic smooth surfaces of R 3. Under a mild uniform sampling condition, we show that the complexity of the 3D Delaunay triangulation of the points is O(N log N).