Approximation of parametric surfaces with discontinuities by discrete smoothing \(D^ m\)-splines. (English) Zbl 0815.65017

Torrens, Juan José

Laurent, Pierre-Jean (ed.) et al., Wavelets, images, and surface fitting. Papers from the 2nd international conference on curves and surfaces, held in Chamonix-Mont-Blanc, France, June 10-16, 1993. Wellesley, MA: A K Peters. 485-492 (1994).

Summary: We study a smoothing method for fitting discontinuous parametric-surfaces when the data points are part of the nodes of a curvilinear grid. This problem may appear, for example, in geophysics, for modelling reverse faults. We proceed as follows. First, a uniform parameterization of the surface is introduced in order to compensate for the absence of a natural parameterization of the data points. An approximating surface is then obtained by solving a minimization problem in a suitable finite element space, whose solution is called discrete smoothing \(D^ m\)-spline. We finally establish the convergence of the method.
For the entire collection see [Zbl 0805.00017].

MSC:

65D10	Numerical smoothing, curve fitting
65D07	Numerical computation using splines
41A15	Spline approximation
41A63	Multidimensional problems

Keywords:

discrete smoothing spline; smoothing; discontinuous parametric-surfaces; finite element; convergence; fitting