Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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
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
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
The Delaunay tetrahedralization from Delaunay triangulated surfaces
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
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Space-time tradeoffs for approximate spherical range counting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An effective condition for sampling surfaces with guarantees
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
An incremental algorithm for reconstruction of surfaces of arbitrary codimension
Computational Geometry: Theory and Applications
Cycle bases of graphs and sampled manifolds
Computer Aided Geometric Design
Maintaining deforming surface meshes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the Locality of Extracting a 2-Manifold in
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
How much geometry it takes to reconstruct a 2-manifold in R3
Journal of Experimental Algorithmics (JEA)
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
SMI 2011: Full Paper: Localized Cocone surface reconstruction
Computers and Graphics
Edge flips and deforming surface meshes
Proceedings of the twenty-seventh annual symposium on Computational geometry
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Bounds on the k-neighborhood for locally uniformly sampled surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
Approximating geodesic distances on 2-manifolds in R3
Computational Geometry: Theory and Applications
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A surface reconstruction algorithm takes as input a set of sample points from an unknown closed and smooth surface in 3-d space, and produces a piece-wise linear approximation of the surface that contains the sample points. Recently, several algorithms with a correctness guarantee have been proposed. They have unfortunately a worst-case running time that is quadratic in the size of the input because they are based on the construction of 3-d Voronoi diagrams or Delaunay tetrahedrizations which can have quadratic size. In this paper, we describe a new algorithm that also has a correctness guarantee but whose worst-case running time is O(n log n) where n is the input size. This is actually optimal. As in some of the previous algorithms, the piece-wise linear approximation produced by the new algorithm is a triangulation which is a subset of the 3-d Delaunay tetrahedrization.