Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
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
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Point-Based Graphics
Robust Smooth Feature Extraction from Point Clouds
SMI '07 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Data-dependent MLS for faithful surface approximation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Robust Voronoi-based curvature and feature estimation
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Delaunay Refinement for Piecewise Smooth Complexes
Discrete & Computational Geometry
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Surface reconstruction with enriched reproducing kernel particle approximation
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
SMI 2013: Voronoi-based feature curves extraction for sampled singular surfaces
Computers and Graphics
Constructing isosurfaces with sharp edges and corners using cube merging
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non-manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we allow the presence of various singularities by requiring that the sampled object is a collection of smooth surface patches with boundaries that can meet or intersect. Our algorithm first identifies and reconstructs the features where singularities occur. Next, it reconstructs the surface patches containing these feature curves. The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs. The global reconstruction is achieved by a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. We provide various experimental results to demonstrate the effectiveness of our feature-preserving singular surface reconstruction algorithm. © 2012 Wiley Periodicals, Inc.