Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2004 Papers
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
Anisotropic point set surfaces
AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
Fast arbitrary splitting of deforming objects
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
ACM SIGGRAPH 2007 papers
Error bounds and optimal neighborhoods for MLS approximation
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Direct boolean intersection between acquired and designed geometry
Computer-Aided Design
Interpolatory point set surfaces—convexity and Hermite data
ACM Transactions on Graphics (TOG)
Splitting meshless deforming objects with explicit surface tracking
Graphical Models
Out-of-core MLS reconstruction
CGIM '07 Proceedings of the Ninth IASTED International Conference on Computer Graphics and Imaging
Polygonizing extremal surfaces with manifold guarantees
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
Bayesian mesh reconstruction from noisy point data
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Curvature estimation of point-sampled surfaces and its applications
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Hardware-accelerated extraction and rendering of point set surfaces
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Surface reconstruction with enriched reproducing kernel particle approximation
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
Noise-adaptive shape reconstruction from raw point sets
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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It is useful to be able to define a two-dimensional point-set surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a three-dimensional subset of R3, a narrow region around the input point cloud. If we were to extend the definition outside the domain, we would produce components of the surface which are far from the point cloud. This is important in practice, since when moving points onto the MLS surface, we need to begin with an initial guess which is within the domain. We visualize the domain in two dimensions, and explain why it is so narrow. We also consider two MLS variants which can be defined on a wider domain without producing spurious surface components. One is efficient and works well except near sharp corners. The other is computationally expensive but seems to work well everywhere.