Volume Data Interpolation using Tensor Products of Spherical and Radial Splines
نویسندگان
چکیده
Trivariate splines solve a special case of scattered data interpolation problem in the volume bounded by two concentric spheres. A triangulation ∆ of the unit sphere S is constructed based on the vertex set V. Given a partition P of the interval [1, R], let Sτ×ρ σ×δ be the space of the spherical splines of degree σ and smoothness τ over ∆ tensored with the univariate radial splines of degree δ and smoothness ρ over P . We use a minimal energy method to find a unique smooth spline s ∈ Sτ×ρ σ×δ interpolating given data values at the points V × P . Numerical investigation is conducted on polynomial reproduction and convergence of the interpolating splines. §
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