Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the conference on Visualization '01
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Shape Dimension and Intrinsic Metric from Samples of Manifolds
Discrete & Computational Geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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)
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Edge flips and deforming surface meshes
Proceedings of the twenty-seventh annual symposium on Computational geometry
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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We present an algorithm to reconstruct a surface from a dense sample. Given n sample points, it runs in O(n log n) time, which is optimal in the pointer machine model. The only existing O(n log n)-time algorithm due to Funke and Ramos uses some sophisticated data structures for the key task of extracting a locally uniform subsample. Our algorithm is based on a variant of the standard octree, and it is much simpler. We built a prototype, which runs an implementation of our algorithm to extract a locally uniform subsample, invokes Cocone to reconstruct a surface from the subsample, and adds back the samples points absent from the subsample via edge flips. The subsample extraction step is very fast and effective. In our experiments with some non-uniform samples, our prototype gives a 51% to 68% speedup from using Cocone alone. Even for locally uniform samples, our prototype is usually much faster.