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
Scattered Data Interpolation Using C2 Supersplines of Degree Six
SIAM Journal on Numerical Analysis
On the Approximation Power of Splines on Triangulated Quadrangulations
SIAM Journal on Numerical Analysis
Macro-elements and stable local bases for splines on Powell-Sabin triangulations
Mathematics of Computation
Minimal energy spherical splines on Clough-Tocher triangulations for Hermite interpolation
Applied Numerical Mathematics
Tri-cubic polynomial natural spline interpolation for scattered data
Calcolo: a quarterly on numerical analysis and theory of computation
Scattered data interpolation by bivariate splines with higher approximation order
Journal of Computational and Applied Mathematics
Scattered noisy Hermite data fitting using an extension of the weighted least squares method
Computers & Mathematics with Applications
Original Article: Spline approximation of gradient fields: Applications to wind velocity fields
Mathematics and Computers in Simulation
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Given a set of scattered data with derivatives values, we use a minimal energy method to find Hermite interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. We show that the minimal energy method produces a unique Hermite spline interpolation of the given scattered data with derivative values. Also we show that the Hermite spline interpolation converges to a given sufficiently smooth function f if the data values are obtained from this f. That is, the surface of the Hermite spline interpolation resembles the given set of derivative values. Some numerical examples are presented to demonstrate our method.