Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Parallel thinning algorithm for binary digital patterns
Handbook of pattern recognition & computer vision
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Proceedings of the conference on Visualization '01
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
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
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Graphical Models
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Learning smooth objects by probing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
An upper bound on the average size of silhouettes
Proceedings of the twenty-second annual symposium on Computational geometry
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Variational tetrahedral meshing
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Learning smooth shapes by probing
Computational Geometry: Theory and Applications
A generic software design for Delaunay refinement meshing
Computational Geometry: Theory and Applications
Reliable implicit surface polygonization using visibility mapping
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
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Delaunay refinement for piecewise smooth complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles
IEEE Transactions on Visualization and Computer Graphics
Maintaining deforming surface meshes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Delpsc: a delaunay mesher for piecewise smooth complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
From Segmented Images to Good Quality Meshes Using Delaunay Refinement
Emerging Trends in Visual Computing
High resolution surface reconstruction from overlapping multiple-views
Proceedings of the twenty-fifth annual symposium on Computational geometry
Proceedings of the twenty-fifth annual symposium on Computational geometry
Technical Section: Variational implicit surface meshing
Computers and Graphics
Cardiac Motion Extraction from Images by Filtering Estimation Based on a Biomechanical Model
FIMH '09 Proceedings of the 5th International Conference on Functional Imaging and Modeling of the Heart
Locally implicit discontinuous Galerkin method for time domain electromagnetics
Journal of Computational Physics
Massive mesh hole repair minimizing user intervention
Computing - Geometric Modelling, Dagstuhl 2008
Surface sampling and the intrinsic Voronoi diagram
SGP '08 Proceedings of the Symposium on Geometry Processing
Feature preserving Delaunay mesh generation from 3D multi-material images
SGP '09 Proceedings of the Symposium on Geometry Processing
High-quality consistent meshing of multi-label datasets
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Shape modeling and analysis with entropy-based particle systems
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
High quality visual hull reconstruction by delaunay refinement
Transactions on computational science IX
High quality visual hull reconstruction by delaunay refinement
Transactions on computational science IX
Fusion of depth maps with multiple scales
Proceedings of the 2011 SIGGRAPH Asia Conference
Virtual interventions for image-based blood flow computation
Computer-Aided Design
Globally optimal spatio-temporal reconstruction from cluttered videos
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
SMI 2012: Short VoxMorph: 3-scale freeform deformation of large voxel grids
Computers and Graphics
Vertex location optimisation for improved remeshing
Graphical Models
Feature-Preserving Reconstruction of Singular Surfaces
Computer Graphics Forum
Rapid sketch modeling of clouds
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Robust and scalable interactive freeform modeling of high definition medical images
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Feature-Preserving, multi-material mesh generation using hierarchical oracles
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
O-snap: Optimization-based snapping for modeling architecture
ACM Transactions on Graphics (TOG)
Fast extraction of high-quality crease surfaces for visual analysis
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Localized delaunay refinement for piecewise-smooth complexes
Proceedings of the twenty-ninth annual symposium on Computational geometry
High quality real-time image-to-mesh conversion for finite element simulations
Proceedings of the 27th international ACM conference on International conference on supercomputing
Screened poisson surface reconstruction
ACM Transactions on Graphics (TOG)
Splat-based surface reconstruction from defect-laden point sets
Graphical Models
High quality real-time Image-to-Mesh conversion for finite element simulations
Journal of Parallel and Distributed Computing
Guaranteed quality tetrahedral Delaunay meshing for medical images
Computational Geometry: Theory and Applications
| Hi-index | 0.01 |
The notion of ε-sample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an ε-sample of a C2-continuous surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an ε-sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose ε-sample. We show that the set of loose ε-samples contains and is asymptotically identical to the set of ε-samples. The main advantage of loose ε-samples over ε-samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes. Given a C2-continuous surface S without boundary, the algorithm generates a sparse ε-sample E and at the same time a triangulated surface Dels(E). The triangulated surface has the same topological type as S, is close to S for the Hausdorff distance and can provide good approximations of normals, areas and curvatures. A notable feature of the algorithm is that the surface needs only to be known through an oracle that, given el line segment, detects whether the segment intersects the surface and in the affirmative, returns the intersection points. This makes the algorithm useful in a wide variety of contexts and for a large class of surfaces.