Approximation by cubic C1-splines on arbitrary triangulations
Numerische Mathematik
Interpolation with piecewise polynomials in more than one variable
Algorithms for approximation
An algorithm for monotone piecewise bicubic interpolation
SIAM Journal on Numerical Analysis
Affine-scaling for linear programs with free variables
Mathematical Programming: Series A and B
Scattered data interpolation in three or more variables
Mathematical methods in computer aided geometric design
A bivariate interpolation algorithm for data that are monotone in one variable
SIAM Journal on Scientific and Statistical Computing
Surface design with minimum energy networks
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Limiting behavior of the affine scaling continuous trajectories for linear programming problems
Mathematical Programming: Series A and B
A note on piecewise monotonic bivariate interpolation
Curves and surfaces
Box spline interpolation; a computational study
Journal of Computational and Applied Mathematics
SIAM Review
Minimal energy surfaces using parametric splines
Computer Aided Geometric Design
Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials
Computer Aided Geometric Design
Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics
SIAM Journal on Numerical Analysis
Scattered Data Interpolation Using C2 Supersplines of Degree Six
SIAM Journal on Numerical Analysis
Computer Aided Geometric Design
Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines
Computer Aided Geometric Design
Scattered Data Interpolation with Multilevel B-Splines
IEEE Transactions on Visualization and Computer Graphics
Shape-preserving approximation of multiscale univariate data by cubic L1 spline fits
Computer Aided Geometric Design
An Efficient Algorithm for Generating Univariate Cubic L1 Splines
Computational Optimization and Applications
Shape-preserving properties of univariate cubic L1 splines
Journal of Computational and Applied Mathematics
Shape-preserving, first-derivative-based parametric and nonparametric cubic L1 spline curves
Computer Aided Geometric Design
A compressed primal-dual method for generating bivariate cubic L1 splines
Journal of Computational and Applied Mathematics
The convergence of three L1 spline methods for scattered data interpolation and fitting
Journal of Approximation Theory
C1 and C2-continuous polynomial parametric Lp splines (p≥1)
Computer Aided Geometric Design
Computer Aided Geometric Design
Computer Aided Geometric Design
Shape-preserving, first-derivative-based parametric and nonparametric cubic L1 spline curves
Computer Aided Geometric Design
A geometric programming approach for bivariate cubic L1 splines
Computers & Mathematics with Applications
Fast L1kCk polynomial spline interpolation algorithm with shape-preserving properties
Computer Aided Geometric Design
Surface Reconstruction and Image Enhancement via $L^1$-Minimization
SIAM Journal on Scientific Computing
Nonlinear L1C1 interpolation: application to Images
Proceedings of the 7th international conference on Curves and Surfaces
Computational Optimization and Applications
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We introduce a class of bi- and multivariate cubic L"1 interpolating splines, the coefficients of which are calculated by minimizing the sum of the L"1 norms of second derivatives. The focus is mainly on bivariate cubic L"1 splines for C^1 interpolation of data located at the nodes of a tensor-product grid. These L"1 splines preserve the shape of data even when the data have abrupt changes in magnitude or spacing. Extensions to interpolation of regularly spaced and scattered bi- and multivariate data by cubic and higher-degree surfaces/hypersurfaces on regular and irregular rectangular/quadrilateral/hexahedral and triangular/tetrahedral grids are outlined.