Convex preserving scattered data interpolation using bivariate \(C^1\) cubic splines

DOI10.1016/S0377-0427(00)00382-4zbMath0966.65016OpenAlexW2090823121MaRDI QIDQ1576461

Ming-Jun Lai

Publication date: 1 August 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00382-4

zbMATH Keywords

interpolationquadratic programmingscattered data interpolationbivariate splinesBernstein-Bézier polynomialsconvexity preserving surface design

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical mathematical programming methods (65K05) Quadratic programming (90C20) Numerical interpolation (65D05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (11)

Approximation of functions on a square by interpolation polynomials at vertices and few Fourier coefficients ⋮ Far-Field Reflector Problem Under Design Constraints ⋮ Smooth bivariate shape-preserving cubic spline approximation ⋮ Scattered data interpolation based upon bivariate recursive polynomials ⋮ Scattered data interpolation with nonnegative preservation using bivariate splines and its application ⋮ Pseudo transient continuation and time marching methods for Monge-Ampère type equations ⋮ The conditions of convexity for Bernstein-Bézier surfaces over triangles ⋮ Convexity-preserving scattered data interpolation scheme using side-vertex method ⋮ Convexity preserving splines over triangulations ⋮ Micro-genetic approach for surface meshing on a set of unorganized points ⋮ Experimental results on quadrangulations of sets of fixed points

Cites Work

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• Scattered data interpolation and approximation using bivariate \(C^{1}\) piecewise cubic polynomials
• The convexity of Bernstein polynomials over triangles
• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
• On convexity of piecewise polynomial functions on triangulations
• Convexity preserving interpolation and Powell-Sabin elements
• Interpolation and approximation from convex sets
• Linear convexity conditions for rectangular and triangular Bernstein-Bézier surfaces
• A counterexample to a theorem about the convexity of Powell--Sabin elements
• On the Approximation Power of Splines on Triangulated Quadrangulations

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