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\(C^1\) Hermite interpolation with PH curves using the Enneper surface. (English) Zbl 1470.65013

Summary: We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular \(C^1\) Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping.

MSC:

65D05 Numerical interpolation
65D17 Computer-aided design (modeling of curves and surfaces)
41A05 Interpolation in approximation theory
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