A note on piecewise blending function interpolation applied to networks of curves in \({\mathbb{R}}^ 3\) (Q1091739)

Let \(F(x_ i(y),y)\), \((i=1,2,...,m)\) and \(F(x,y_ j(x))\), \((j=1,2,...,n)\) be two given families of curves on a continuous surface F(x,y) in \({\mathbb{R}}^ 3\). For these given known two families \(F(x_ i(y),y)\) and \(F(x,y_ j(x))\), the author constructs good interpolators, using piecewise cubic Hermite polynomials or cubic splines. Finally the author compares his algorithm with \textit{J. A. Wixom}'s one [SIAM J. Numer. Anal. 15, 1178-1193 (1978; Zbl 0401.65005)].