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\(C^2\) Hermite interpolation by Pythagorean hodograph space curves. (English) Zbl 1122.65016

The problem of \(C^2\) Hermite interpolation by Pythagorean hodograph (PH) space curves is solved. Namely, for any set of \(C^2\) space boundary data a four-dimensional family of PH interpolants of degree 9 is constructed. The particular solution that fulfils a kind of geometrically invariant parameterization is isolated from the family which is shown to preserve planarity, has the best possible approximation order 6 and has symmetry property regarding the data order reverse. Some applications are quoted.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
53A04 Curves in Euclidean and related spaces
65D05 Numerical interpolation
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