On the angular defect of triangulations and the pointwise approximation of curvatures

DOI10.1016/S0167-8396(03)00077-3zbMath1069.65544MaRDI QIDQ2388515

Vincent Borrelli, Jean-Marie Morvan, Frédéric Cazals

Publication date: 14 September 2005

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

zbMATH Keywords

approximationsdifferential geometrymeshescurvaturessmooth surfaces

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Surfaces in Euclidean and related spaces (53A05)

Related Items (14)

Ternary univariate curvature-preserving subdivision ⋮ Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics ⋮ Region selection in Markov random fields: Gaussian case ⋮ An analysis and comparison of parameterization-based computation of differential quantities for discrete surfaces ⋮ High-Order Approximation of Gaussian Curvature with Regge Finite Elements ⋮ Error term in pointwise approximation of the curvature of a curve ⋮ Principal curvature measures estimation and application to 3D face recognition ⋮ Variational Methods for Discrete Geometric Functionals ⋮ Discrete schemes for Gaussian curvature and their convergence ⋮ Generalized shape operators on polyhedral surfaces ⋮ High order surface radiation conditions for time-harmonic waves in exterior domains ⋮ Illustrative visualization: Interrogating triangulated surfaces ⋮ Estimating differential quantities using polynomial fitting of osculating jets ⋮ Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces

Cites Work

• On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
• Surface reconstruction by Voronoi filtering
• On the approximation of a smooth surface with a triangulated mesh
• On the curvature of piecewise flat spaces
• Critical points and curvature for embedded polyhedra
• Theory of Shell Structures
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