2 research outputs found
Interpolation and scattered data fitting on manifolds using projected PowellāSabin splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(UĪ¾ , Ī¾)}Ī¾ā satisfying certain conditions of smooth dependence on Ī¾. If is a C2-manifold embedded into R3, then projections into tangent planes can be employed. The data fitting method is a two-stage method. We prove that the resulting function on the manifold is continuously differentiable, and establish error bounds for both methods for the case when the data are generated by a smooth function