Wang, Tianjun A \(C^ 2\)-quintic spline interpolation scheme on triangulation. (English) Zbl 0770.65005 Comput. Aided Geom. Des. 9, No. 5, 379-386 (1992). The author presents an explicitly given quintic piecewise polynomial \(C^ 2\) interpolation scheme for triangular data. The scheme is obtained on the subdivided triangulation with the minimal split (each original triangle into 7 subtriangles). The paper thus gives an affirmative answer to a known question. Reviewer: B.D.Bojanov (Sofia) Cited in 12 Documents MSC: 65D07 Numerical computation using splines 65D05 Numerical interpolation 41A05 Interpolation in approximation theory 41A15 Spline approximation 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX) Keywords:bivariate interpolation; triangulation; minimal split; scattered data; quintic; spline function; Bernstein-Bézier form; Bézier net PDF BibTeX XML Cite \textit{T. Wang}, Comput. Aided Geom. Des. 9, No. 5, 379--386 (1992; Zbl 0770.65005) Full Text: DOI References: [1] Alfeld, P., A bivariate C2 clough-tocher scheme, Computer aided geometric design, 1, 257-267, (1984) · Zbl 0597.65005 [2] Cui, C.K.; Wang, R.H., On smooth multivariate spline functions, Math. of computation, 41, 163, 131-142, (1983) · Zbl 0542.41008 [3] de Boor, C., B-form basics, (), 131-148 [4] Farin, G., Bézier polynomials over triangles and the construction of piecewise Cr polynomials, Technical report TR/91, (1980), Brunel University Uxbridge, England [5] Farin, G., Triangular Bernstein-Bézier patches, Computer aided geometric design, 3, 2, 83-128, (1986) [6] Jia, R.Q., B-net representation of multivariate splines, Kexue tongbao, 33, 10, 807-811, (1988) · Zbl 0687.41019 [7] Schumaker, L.L., On the dimension of space of piecewise polynomials in two variables, (), 396-412 [8] Shi, X.Q., Higher-dimensional splines, Ph.D. dissertation, (1988), Jilin University Changchun, P.R. of China This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.