Best Near-Interpolation by Curves: Existence
SIAM Journal on Numerical Analysis
On the problems of smoothing and near-interpolation
Mathematics of Computation
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
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We consider existence of curves c:[0, 1] → Rn which minimize an energy of the form ∫ ||c(k)||p (k = 1,2 ..... 1 p ∞) under side-conditions of the form Gj(c(t1, j)...., c(k-1)(tk,j)) ∈ Mj, where Gj is a continuous function, ti,j ∈ [0, 1], Mj is some closed set, and the indices j range in some index set J. This includes the problem of finding energy minimizing interpolants restricted to surfaces, and also variational near-interpolating problems. The norm used for vectors does not have to be Euclidean.It is shown that such an energy minimizer exists if there exists a curve satisfying the side conditions at all, and if among the interpolation conditions there are at least k points to be interpolated. In the case k = 1, some relations to arc length are shown.