Some applications of discrete \(D^ m\) splines. (English) Zbl 0676.41012

Arcangéli, R.

Mathematical methods in computer aided geometric design, Pap. Int. Conf., Oslo/Norw. 1988, 35-44 (1989).

Summary: [For the entire collection see Zbl 0669.00011.]
Given a suitable finite element space \(V_ h\), we define \(``V_ h\)- discrete smoothing \(D^ 2\)-splines” belonging to \(V_ h\). Then we give three non-trivial examples of utilization of these splines: 1) construction of surfaces of class \(C^ 1\) or \(C^ 2\) from a large number of scattered Lagrange data, 2) approximation of non regular functions (a problem occurring in geophysics), and 3) spline fitting along a curve (an attempt to model the construction of surfaces from iso- valued curves).

MSC:

41A15

Spline approximation

Keywords:

smoothing \(D^ 2\)-splines

Citations:

Zbl 0669.00011