Convexity preserving interpolation

DOI10.1016/S0167-8396(98)00042-9zbMath0909.68183MaRDI QIDQ1274469

Aidi Li

Publication date: 12 January 1999

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

zbMATH Keywords

multivariate interpolationconvexity preserving\(C^{1}\)-piecewise cubic interpolants\(C^{1}\)-piecewise quadratic interpolants

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (11)

Approximations of differentiable convex functions on arbitrary convex polytopes ⋮ Smooth bivariate shape-preserving cubic spline approximation ⋮ Scattered data interpolation based upon bivariate recursive polynomials ⋮ Suitability of Parametric Shepard Interpolation for Nonrigid Image Registration ⋮ Convexity preserving scattered data interpolation using Powell-Sabin elements ⋮ The conditions of convexity for Bernstein-Bézier surfaces over triangles ⋮ On the convexity of piecewise-defined functions ⋮ On the convexity of Bézier nets of quadratic Powell-Sabin splines on 12-fold refined triangulations ⋮ Convexity-preserving scattered data interpolation scheme using side-vertex method ⋮ Interpolation with slackness and continuity control and convexity-preservation using singular blending ⋮ Convexity preserving splines over triangulations

Cites Work

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• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
• The complexity of interpolating given data in three space with a convex function of two variables
• Approximation by cubic \(C^ 1\)-splines on arbitrary triangulations
• Bounds on the dimension of spaces of multivariate piecewise polynomials
• Convexity preserving interpolation and Powell-Sabin elements
• A counterexample to a theorem about the convexity of Powell--Sabin elements
• Piecewise Quadratic Approximations on Triangles

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