The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Proceedings of the sixth ACM symposium on Solid modeling and applications
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Estimating surface normals in noisy point cloud data
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
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Shape segmentation using local slippage analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
On the normal vector estimation for point cloud data from smooth surfaces
Computer-Aided Design
Comparison of surface normal estimation methods for range sensing applications
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Technical Section: Robust normal estimation for point clouds with sharp features
Computers and Graphics
Polygonizing extremal surfaces with manifold guarantees
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Normal estimation for point clouds: a comparison study for a Voronoi based method
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
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We present an algorithm for robustly analyzing point data arising from sampling a 2D surface embedded in 3D, even in the presence of noise and non-uniform sampling. The algorithm outputs, for each data point, a surface normal, a local surface approximation in the form of a one-ring, the local shape (flat, ridge, bowl, saddle, sharp edge, corner, boundary), the feature size, and a confidence value that can be used to determine areas where the sampling is poor or not surface-like. We show that the normal estimation out-performs traditional fitting approaches, especially when the data points are non-uniformly sampled and in areas of high curvature. We demonstrate surface reconstruction, parameterization, and smoothing using the one-ring neighborhood at each point as an approximation of the full mesh structure.