Affine-scaling for linear programs with free variables
Mathematical Programming: Series A and B
The variational approach to shape preservation
Curves and surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics
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
Shape preserving interpolatory subdivision schemes for nonuniform data
Journal of Approximation Theory
An Efficient Algorithm for Generating Univariate Cubic L1 Splines
Computational Optimization and Applications
Tensorial Rational Surfaces with Base Points via Massic Vectors
SIAM Journal on Numerical Analysis
Shape-preserving properties of univariate cubic L1 splines
Journal of Computational and Applied Mathematics
A compressed primal-dual method for generating bivariate cubic L1 splines
Journal of Computational and Applied Mathematics
C1 and C2-continuous polynomial parametric Lp splines (p≥1)
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
Shape-preserving, multiscale interpolation by bi- and multivariate cubic L1 splines
Computer Aided Geometric Design
Nonlinear L1C1 interpolation: application to Images
Proceedings of the 7th international conference on Curves and Surfaces
Computational Optimization and Applications
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In this article, we address the problem of interpolating data points by regular L"1-spline polynomial curves of smoothness C^k, k=1, that are invariant under rotation of the data. To obtain a C^1 cubic interpolating curve, we use a local minimization method in parallel on five data points belonging to a sliding window. This procedure is extended to create C^k-continuous L"1 splines, k=2, on larger windows. We show that, in the C^k-continuous (k=1) interpolation case, this local minimization method preserves the linear parts of the data well, while a global L"1 minimization method does not in general do so. The computational complexity of the procedure is linear in the global number of data points, no matter what the order C^k of smoothness of the curve is.