\(C^2\)- (\(C^3\)-)continuous interpolation spline curve and surface
The authors develop an approach to the regular interpolation of given 2D or 3D data which are ordered in a certain reasonable way. The interpolants are constructed by tensor products of one-dimensional splines. At first a method of \(C^2\) biquintic composite surfaces is presented. Then a \(C^3\) interpolation spline surface construction method is considered. Some desirable properties of the presented interpolation schemes, such as second-order or third-order continuity, locality, readiness of implementation, are established. Finally, a numerical example to illustrate the new method is given.
scientific article; zbMATH DE number 1164239