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On G 2 Continuous Spline Interpolation of Curves in ℝd

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Abstract

In this paper the problem of G 2 continuous interpolation of curves in ℝd by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ℝd. In this case the optimal approximation order is also determined.

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  1. Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia

    Emil Žagar

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  1. Emil Žagar
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Žagar, E. On G 2 Continuous Spline Interpolation of Curves in ℝd . BIT Numerical Mathematics 42, 670–688 (2002). https://doi.org/10.1023/A:1021940117897

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