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
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
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
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Graphical Models - Special issue on SMI 2004
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The notion of ε-sample, as 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 smooth 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.