Bernstein-Be´zier polynomials on spheres and sphere-like surfaces
Computer Aided Geometric Design
Dimension and local bases of homogeneous spline spaces
SIAM Journal on Mathematical Analysis
Fitting scattered data on sphere-like surfaces using spherical splines
Journal of Computational and Applied Mathematics - Special issue on scattered data
Hybrid Be´zier patches on sphere-like surfaces
Journal of Computational and Applied Mathematics - Special issue on scattered data
Filling polygonal holes using C1 cubic triangular spline patches
Computer Aided Geometric Design
Spherical Splines for Data Interpolation and Fitting
SIAM Journal on Scientific Computing
Energy minimization method for scattered data Hermite interpolation
Applied Numerical Mathematics
On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Scattered data fitting on surfaces using projected Powell-Sabin splines
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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We present a study of the minimal energy method applied to the Hermite interpolation problem over Clough-Tocher partitions on the unit sphere. A subset of spline coefficients is found by satisfying nodal interpolating conditions. The rest of the coefficients are found through energy minimization subject to C^1 conditions. We show that the error in approximation of a given sufficiently smooth function by the minimal energy Hermite interpolating spline depends on the mesh size of the underlying triangulation cubically. In addition, we prove that minimizers of energy functionals with different homogeneous extensions are equivalent in the sense that they all converge to the sampled function, and the order of convergence is independent of the extension. We conclude with numerical examples.