Abstract
Using quartic splines on refined grids, we present a method for convexity preservingC 2 interpolation which is successful for all strictly convex data sets. In the first stage, one suitable additional knot in each subinterval of the original data grid is fixed dependent on the given data values. In the second stage, a visually pleasant interpolant is selected by minimizing an appropriate choice functional.
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Communicated by C. Brezinski
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Mulansky, B., Schmidt, J.W. Constructive methods in convexC 2 interpolation using quartic splines. Numer Algor 12, 111–124 (1996). https://doi.org/10.1007/BF02141744
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DOI: https://doi.org/10.1007/BF02141744
Keywords
- Shape preserving interpolation
- convex interpolation
- monotonicity and range restrictions
- quarticC 2 splines on refined grids
- additional knots
- choice functionals