Construction of surfaces by discrete variational splines with parallelism conditions

AbstractWe present in this paper a discrete problem of constructing some parametric surfaces with parallelism conditions from some given Lagrangean data. We consider the problem of fitting some scattered points with a surface pseudo-parallel to a given reference surface in a finite element space. Some convergence results are shown. Finally, we analyze some graphical examples in order to prove the validity and the effectiveness of this method

Approximation of explicit surfaces by fairness bicubic variational splines

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of explicit surfaces is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is established. We analyze some numerical and graphical examples in order to show the validity of our method

Approximation of Curves by Fairness Cubic Splines

Abstract In this paper we present an approximation method of curves by a new type of spline functions called fairness cubic splines from a given Lagrangian data set under fairness constraints. An approximating problem of curves is obtained by minimizing a quadratic functional in a parametric space of cubic splines. This method is justified by a convergence result and an analysis of some numerical and graphical examples