Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Systems of coordinates associated with points scattered in the plane
Computer Aided Geometric Design
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
r-regular shape reconstruction from unorganized points
Computational Geometry: Theory and Applications - special issue on applied computational geometry
Accurate and efficient unions of balls
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
Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
Proceedings of the Workshop on Geometry and Robotics
A local coordinate system on a surface
Proceedings of the seventh ACM symposium on Solid modeling and applications
A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Undersampling and oversampling in sample based shape modeling
Proceedings of the conference on Visualization '01
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Provably good surface sampling and approximation
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Delaunay triangulations approximate anchor hulls
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Provably good moving least squares
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
An effective condition for sampling surfaces with guarantees
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Normal cone approximation and offset shape isotopy
Computational Geometry: Theory and Applications
Recovering structure from r-sampled objects
SGP '09 Proceedings of the Symposium on Geometry Processing
Edge flips and deforming surface meshes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Normal and feature approximations from noisy point clouds
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Discrete bi-Laplacians and biharmonic b-splines
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
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Natural neighbor coordinates and natural neighbor interpolation have been introduced by Sibson for interpolating multivariate scattered data. In this paper, we consider the case where the data points belong to a smooth surface S, i.e., a (d-1)-manifold of R^d. We show that the natural neighbor coordinates of a point X belonging to S tends to behave as a local system of coordinates on the surface when the density of points increases. Our result does not assume any knowledge about the ordering, connectivity or topology of the data points or of the surface. An important ingredient in our proof is the fact that a subset of the vertices of the Voronoi diagram of the data points converges towards the medial axis of S when the sampling density increases.