Nonpolynomial (X, A, φ)-splines of the third order and the special case of B_φ-splines of class C~2 are studied. For such splines calibration relations are obtained, owing to which the coordinate splines on the original grid is represented in terms of the coordinate splines on a refined grid. A nonlinear mapping (R~4)~9 |→ R~4 and locally orthogonal chains of vectors are used for this purpose.
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