Minimal energy -surfaces on uniform Powell-Sabin type meshes

Optimization of parameters for curve interpolation by cubic splines

“…Let us prove the existence and the uniqueness of the solution of the problem (6). Before doing so, we need the following result.…”

“…Such a functional may represent minimal energy [6], or physical consideration such as minimization of the air of a surface, or minimization of the curvature or variation of curvature (see [7]). These techniques have many applications in CAD, CAGD and Earth Sciences.…”

Minimal energy Cr-surfaces on uniform Powell–Sabin-type meshes for noisy data

“…A wide range of functionals have been proposed from physical considerations (see [2,8] and references therein), obtaining variational surfaces by the minimization in an adequate functional space of a quadratic functional that contains some terms associated with Sobolev semi-norms. In all cases, some smoothing parameters appear in the definition of the minimization functional.…”

“…In all cases, some smoothing parameters appear in the definition of the minimization functional. The estimation of optimal values of these parameters that minimize a given measure is an important problem that has been studied, for example in [5,13,15] for noisy data, and in [2] for exact data.…”

“…In this work we present, following the method given in [2], a method to obtain, for noisy data, a C r -surface (for any r 1) on a polygonal domain D ⊂ R 2 which approximates a Lagrangian data set, and minimizes an "energy functional" in which the degree of smoothness is measured by a linear combination of the usual semi-norms | · | m , for m = 1, . .…”