Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
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
Rational curves and surfaces: applications to CAD
Rational curves and surfaces: applications to CAD
Bernstein-Be´zier polynomials on spheres and sphere-like surfaces
Computer Aided Geometric Design
Fitting scattered data on sphere-like surfaces using spherical splines
Journal of Computational and Applied Mathematics - Special issue on scattered data
Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics
SIAM Journal on Numerical Analysis
Scattered data fitting on the sphere
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere
SIAM Journal on Scientific Computing
Computer Aided Geometric Design
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
The convergence of three L1 spline methods for scattered data interpolation and fitting
Journal of Approximation Theory
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We investigate C1-smooth bivariate curvature-based cubic L1 interpolating splines in spherical coordinates. The coefficients of these splines are calculated by minimizing an integral involving the L1 norm of univariate curvature in four directions at each point on the unit sphere. We compare these curvature-based cubic L1 splines with analogous cubic L2 interpolating splines calculated by minimizing an integral involving the square of the L2 norm of univariate curvature in the same four directions at each point. For two sets of irregular data on an equilateral tetrahedron with protuberances on the faces, we compare these two types of curvature-based splines with each other and with cubic L1 and L2 splines calculated by minimizing the L1 norm and the square of the L2 norm, respectively, of second derivatives. Curvature-based cubic L1 splines preserve the shape of irregular data well, better than curvature-based cubic L2 splines and than second-derivative-based cubic L1 and L2 splines. Second-derivative-based cubic L2 splines preserve shape poorly. Variants of curvature-based L1 and L2 splines in spherical and general curvilinear coordinate systems are outlined.