The geometry of fractal sets
Introduction to algorithms
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Computational Geometry: Theory and Applications
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd 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
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Surface reconstruction with anisotropic density-scaled alpha shapes
Proceedings of the conference on Visualization '98
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
r-regular shape reconstruction from unorganized points
Computational Geometry: Theory and Applications - special issue on applied computational geometry
Curve reconstruction, the traveling salesman problem and Menger's theorem on length
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
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
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
New techniques for topologically correct surface reconstruction
Proceedings of the conference on Visualization '00
An integrating approach to meshing scattered point data
Proceedings of the 2005 ACM symposium on Solid and physical modeling
A composite approach to meshing scattered data
Graphical Models - Special issue on SPM 05
Reconstruction with Voronoi centered radial basis functions
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On the normal vector estimation for point cloud data from smooth surfaces
Computer-Aided Design
LS-RBF network based 3D surface reconstruction method
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
A heuristic approach to reconstruct triangle mesh from unorganized point cloud
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 5
SMI 2011: Full Paper: Point set silhouettes via local reconstruction
Computers and Graphics
Visible neighborhood graph of point clouds
Graphical Models
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
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We present a new approach to surface reconstruction in arbitrary dimensions based on the Delaunay complex. Basically, our algorithm picks locally a surface at each vertex. In the case of two dimensions we prove that this method gives indeed a reconstruction scheme. In three dimensions we show that for smooth regions of the surface this method works well and at difficult parts of the surface yields an output well-suited for postprocessing. As a postprocessing step we propose a topological clean up and a new technique based on linear programming in order to establish a topologically correct surface. These techniques should be useful also for many other reconstruction algorithms.