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
An implicit surface polygonizer
Graphics gems IV
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
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
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
A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces
Discrete & 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
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
A point-based approach to PDE-Based surface reconstruction
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Isometry-invariant matching of point set surfaces
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
Approximating geodesics on point set surfaces
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
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We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least-squares approach. It can be evaluated very fast, but artifacts are significantly reduced. We propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG), for which we propose several extensions. The proximity graph also allows us to estimate the local sampling density, which we utilize to automatically adapt the bandwidth of the kernel and to detect boundaries. Consequently, our method is able to handle point clouds of varying sampling density without manual tuning. Our method can be integrated into other surface definitions, such as moving least squares, so that these benefits carry over.