The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A-shapes of a finite point set
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Proceedings of the sixth ACM symposium on Solid modeling and applications
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees
Computational Geometry: Theory and Applications
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Automatic recognition of 2D shapes from a set of points
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part I
Shape reconstruction from an unorganized point cloud with outliers
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
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This paper deals with the problem of reconstructing with guarantees an open subset Ω of Rd from an unorganized set S of sample points non-uniformly distributed inside Ω and not just lying on its boundary. We are able to select a subset of S making sense of what could be the boundary of a point cloud. The definition of this boundary is simple and there is an efficient algorithm to compute it. Under given conditions, we prove that this boundary carries topological and geometrical properties of Omega.