A C1 composite spline Hermite interpolant on the sphere

Abstract

In this paper, we identified the sphere‐like surface by a rectangular domain. We constructed a new interpolant on the sphere using the tensor product of the quadratic composite‐spline interpolant and the third‐order trigonometric composite‐spline interpolant. This construction on the rectangular domain is described in detail, with the study and the proof of the error bounds of each interpolant. Furthermore, we present numerical examples to show the efficiency of this method.

Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks

“…and B 0,j (u 0 , v) = B j (v|V) [23,24], from ( 1), ( 5) and ( 16), we get (11). Similarly, by setting u = u m+1 in (4), since i R+1 = m + 1, ( 12) follows.…”

“…Tensor product B-spline surfaces, despite their limits, due to the parametric domain rectangular topology, can be a good tool in CAGD since they are quite simple to use and not too tightly constrained for the object shape in some cases (see e.g., [10,11] (Chapter 10)). Possible unwanted oscillations can be produced by their high coordinate degree, but they can be successfully avoided by smooth parametric surfaces on triangulations, having a lower total degree [12][13][14].…”