A new approach for the geometrical optimization of five-axis-movement is presented in this paper. Regarding a fiveaxis-movement with large tolerances for lead and tilt-angle for example in the case of laser-cutting there are endless ways of generating motions without violating the orientation-tolerances. By regarding the movement of the involved axes it is shown that for a given 5-axis trajecto...

Given an m-dimensional surface Φ in R, we characterize parametric curves in Φ, which interpolate or approximate a sequence of given points p i ∈ Φ and minimize a given energy functional. As energy functionals we study familiar functionals from spline theory, which are linear combinations of L norms of certain derivatives. The characterization of the solution curves is similar to the well-known ...

The aim of this study is to obtain numerical solutions the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. used convert original into two sub equations including linear and nonlinear part as a slight modification idea. After progress, reduce algebraic systems. For purpose, quintic B-spline base functions are polynomial approximat...

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

We propose a construction of trivariate C 1 spline functions over a special tetrahedron partition and compare our construction with other known constructions of C 1 spline functions which are summarized in this paper. We improve the Alfeld construction of C 1 quintic spline spaces. For those polygonal domains in R 3 which admit the special tetrahedron partition, our construction provides a more...

A piecewise quintic G1 spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular Bézier representation, is affine invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G1 continuously around a common vertex is solved by constru...

In this paper, a new difference scheme based on C1-quintic splines is derived for the numerical solution of the stiff delay differential equations. Convergence results shows that the methods have a convergence of order five. Moreover, the stability analysis properties of these methods have been studied. Finally, numerical results illustrating the behavior of the methods when faced with some dif...