A simple algorithm for homeomorphic surface reconstruction
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
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Generalized Curvatures
ACM SIGGRAPH 2009 papers
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Convergence of discrete Laplace-Beltrami operators over surfaces
Computers & Mathematics with Applications
Feature-preserving mesh denoising based on vertices classification
Computer Aided Geometric Design
Convergence analysis of discrete differential geometry operators over surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Graphical Models
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This work concerns the approximation of the shape operator of smooth surfaces in R^3 from polyhedral surfaces. We introduce two generalized shape operators that are vector-valued linear functionals on a Sobolev space of vector fields and can be rigorously defined on smooth and on polyhedral surfaces. We consider polyhedral surfaces that approximate smooth surfaces and prove two types of approximation estimates: one concerning the approximation of the generalized shape operators in the operator norm and one concerning the pointwise approximation of the (classic) shape operator, including mean and Gaussian curvature, principal curvatures, and principal curvature directions. The estimates are confirmed by numerical experiments.