Planar cubic G interpolatory splines with small strain energy
نویسندگان
چکیده
In this paper, a classical problem of the construction of a cubic G1 continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. They are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally and is regular, cusp-, loopand fold-free. Numerical examples demonstrate that it is satisfactory as far as the shape of the curve is concerned.
منابع مشابه
Planar cubic G1 interpolatory splines with small strain energy
In this paper, a classical problem of the construction of a cubic G1 continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. They are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally and...
متن کاملCurvature variation minimizing cubic Hermite interpolants
In this paper, planar parametric Hermite cubic interpolants with small curvature variation are studied. By minimization of an appropriate approximate functional, it is shown that a unique solution of the interpolation problem exists, and has a nice geometric interpretation. The best solution of such a problem is a quadratic geometric interpolant. The optimal approximation order 4 of the solutio...
متن کاملPlanar cubic Hermite G splines with small strain energy
In this paper, a classical problem of the construction of a cubic Hermite G1 continuous spline curve is considered. The only data given are interpolation points, while tangent directions are unknown. They are constructed in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is regular, cusp-, loopand fold-free. Even more, it...
متن کاملScattered data interpolation by bivariate splines with higher approximation order
Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...
متن کاملOn interpolatory divergence-free wavelets
We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct ...
متن کامل