Convexity preserving interpolation and Powell-Sabin elements

DOI10.1016/0167-8396(92)90035-NzbMath0760.65005OpenAlexW1992654770MaRDI QIDQ1200984

Wolfgang Dahmen, J. M. Carnicer

Publication date: 17 January 1993

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

Full work available at URL: https://doi.org/10.1016/0167-8396(92)90035-n

zbMATH Keywords

finite elementsconvexitymultivariate interpolationPowell-Sabin elementsadaptative least squares algorithmconvex interpolantsmodeling of curves

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

Multivariate convexity preserving interpolation by smooth functions, Surface fitting using convex tensor-product splines, Interpolation and approximation from convex sets, Quadratic spline quasi-interpolants on Powell-Sabin partitions, A counterexample to a theorem about the convexity of Powell--Sabin elements, Convexity preserving scattered data interpolation using Powell-Sabin elements, On the convexity of Bézier nets of quadratic Powell-Sabin splines on 12-fold refined triangulations, Sectional-curvature preserving skinning surfaces, Piecewise linear interpolants to Lagrange and Hermite convex scattered data, Convexity-preserving scattered data interpolation scheme using side-vertex method, Convexity preserving splines over triangulations, On a class of polynomial triangular macro-elements, Convexity preserving interpolation, Convex preserving scattered data interpolation using bivariate \(C^1\) cubic splines, Numerical Approximation of the Value of a Stochastic Differential Game with Asymmetric Information

Cites Work

• The complexity of interpolating given data in three space with a convex function of two variables
• Voronoi diagrams and arrangements
• On convexity of piecewise polynomial functions on triangulations
• On Shape Preserving Quadratic Spline Interpolation
• Error Bounds for Hermite Interpolation by Quadratic Splines on an  -Triangulation
• Piecewise Quadratic Approximations on Triangles
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