Convexity-preserving interpolatory subdivision

DOI10.1016/0167-8396(94)90023-XzbMath0790.65005OpenAlexW2026088070MaRDI QIDQ1315804

Alain Le Méhauté, Florencio I. Utreras

Publication date: 23 June 1994

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

Full work available at URL: https://doi.org/10.1016/0167-8396(94)90023-x

zbMATH Keywords

numerical examplesshape preservationcomputer aided geometric designsubdivision algorithmpreservation of convexitycurve and surface generationiterative knot insertionshape preserving function interpolation

Mathematics Subject Classification ID

Numerical interpolation (65D05) Approximation with constraints (41A29) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (15)

The four-point interpolation subdivision curve is neither convex nor concave in all but one case ⋮ Ternary univariate curvature-preserving subdivision ⋮ A geometric look at corner cutting ⋮ Incenter subdivision scheme for curve interpolation ⋮ A new four-point shape-preserving \(C^3\) subdivision scheme ⋮ Sectional-curvature preserving skinning surfaces ⋮ A variational approach to subdivision ⋮ Normal based subdivision scheme for curve design ⋮ Shape-preserving interpolation by splines using vector subdivision ⋮ Conditions on shape preserving of stationary polynomial reproducing subdivision schemes ⋮ A class of shape preserving 5-point n-ary approximating schemes ⋮ A note on convexity-preserving interpolation subdivision ⋮ On convex quadratic approximation ⋮ Shape preserving interpolatory subdivision schemes for nonuniform data ⋮ A new class of \(2m\)-point binary non-stationary subdivision schemes

Uses Software

• pchip

Cites Work

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• Monotone interpolation of scattered data in \({\mathbb{R}}^ s\)
• Algorithms for computing shape-preserving spline approximations to data
• Constrained \(L_ p\) approximation
• Constrained interpolation and smoothing
• A 4-point interpolatory subdivision scheme for curve design
• Interpolation by smooth functions under restrictions on the derivatives
• Taylorian fields and subdivision algorithms
• Shape-Preserving Bivariate Interpolation
• On Shape Preserving Quadratic Spline Interpolation
• Monotone Piecewise Bicubic Interpolation
• Monotonicity Preserving Surface Interpolation
• Co-Monotone Interpolating Splines of Arbitrary Degree—a Local Approach
• Smoothing and Interpolation in a Convex Subset of a Hilbert Space
• Monotone Piecewise Cubic Interpolation
• Constrained Interpolation
• On Monotone and Convex Spline Interpolation

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