Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Computing the medial surface of a solid from a domain Delaunay triangulation
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Algorithmic geometry
Accurate and efficient unions of balls
Proceedings of the sixteenth annual symposium on Computational geometry
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
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
Delaunay triangulation programs on surface data
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Deformable Solid Modeling using Sampled Medial Surfaces: A Multiscale Approach
Deformable Solid Modeling using Sampled Medial Surfaces: A Multiscale Approach
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
The probabilistic complexity of the Voronoi diagram of points on a polyhedron
Proceedings of the eighteenth annual symposium on Computational geometry
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes
Computational Geometry: Theory and Applications
A geometric convection approach of 3-D reconstruction
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
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
3-Dimensional minimum energy broadcasting problem
Ad Hoc Networks
3-D minimum energy broadcasting
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay triangulation of such point sets. Although the complexity of the Delaunay triangulation of points may be quadratic in the worst-case, we show in this paper that it is only linear when the points are distributed on a fixed number of well-sampled facets (e.g. the facets of a polyhedron). Our bound is deterministic and the constants are explicitly given.