Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
The expected size of the sphere-of-influence graph
Computational Geometry: Theory and Applications
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Curve reconstruction from unorganized points
Computer Aided Geometric Design
Surfels: surface elements as rendering primitives
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Visualization and Computer Graphics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Surface Reconstruction Using Adaptive Clustering Methods
Geometric Modelling
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Sphere of influence graphs and the L∞-metric
Discrete Applied Mathematics
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Combining edges and points for interactive high-quality rendering
ACM SIGGRAPH 2003 Papers
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating Bounded, Non-Orientable Surfaces from Points
SMI '04 Proceedings of the Shape Modeling International 2004
ACM SIGGRAPH 2004 Papers
Sphere-of-influence graphs using the sup-norm
Mathematical and Computer Modelling: An International Journal
Free-form modelling for surface inpainting
AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Fast arbitrary splitting of deforming objects
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Splitting meshless deforming objects with explicit surface tracking
Graphical Models
Visible neighborhood graph of point clouds
Graphical Models
Detail-preserving surface inpainting
VAST'05 Proceedings of the 6th International conference on Virtual Reality, Archaeology and Intelligent Cultural Heritage
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We present a new definition of an implicit surface over a noisy point cloud. It can be evaluated very fast, but, unlike other definitions based on the moving least squares approach, it does not suffer from artifacts. In order to achieve robustness, we propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. The starting point in the graph is determined by approximate nearest neighbor search. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG). For both, we propose to use modifications, the r-SIG and the pruned Delaunay graph. We have implemented our new surface definition as well as a test environment which allows to visualize and to evaluate the quality of the surfaces. We have evaluated the different surfaces induced by different proximity graphs. The results show that artifacts and the root mean square error are significantly reduced.