Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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
Shape transformation using variational implicit functions
Proceedings of the 26th 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
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the sixth ACM symposium on Solid modeling and applications
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Provably good surface sampling and approximation
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Progressive point set surfaces
ACM Transactions on Graphics (TOG)
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
ACM SIGGRAPH 2004 Papers
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Registration of point cloud data from a geometric optimization perspective
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Fast low-memory streaming MLS reconstruction of point-sampled surfaces
Proceedings of Graphics Interface 2009
A new mesh-growing algorithm for fast surface reconstruction
Computer-Aided Design
Wavelet frame based surface reconstruction from unorganized points
Journal of Computational Physics
An adaptive normal estimation method for scanned point clouds with sharp features
Computer-Aided Design
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We analyze a moving least squares (MLS) interpolation scheme for reconstructing a surface from point cloud data. The input is a sufficiently dense set of sample points that lie near a closed surface F with approximate surface normals. The output is a reconstructed surface passing near the sample points. For each sample point s in the input, we define a linear point function that represents the local shape of the surface near s. These point functions are combined by a weighted average, yielding a three-dimensional function I. The reconstructed surface is implicitly defined as the zero set of I. We prove that the function I is a good approximation to the signed distance function of the sampled surface F and that the reconstructed surface is geometrically close to and isotopic to F. Our sampling requirements are derived from the local feature size function used in Delaunay-based surface reconstruction algorithms. Our analysis can handle noisy data provided the amount of noise in the input dataset is small compared to the feature size of F.