Abstract
Based on the work of Robin Sibson concerning Natural Neighbor Interpolant, this paper is devoted to incorporate this concept in Spline theory. To do this, first a new concept, the “Covering Spheres”, is presented, which is then linked with Sibson's interpolant. Finally, the interpolant is reformulated to present it as a Bernstein polynomial in local coordinates instead of the usual presentation as rational quartics. As a corollary, the whole idea is presented as modified Vertex Splines.
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