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...

In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates the solutions, and their higher order derivatives of differential equations. Numerical illustrations are tabulated to demonstrate the practical usefulness of ...

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...

The interpolation of a planar sequence of points p0, . . . , pN by shape-preserving G 1 or G2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting ‘tension’ parameters that arise upon relaxing parametric continuity to geometric continuity. In the G2 case, the PH spline construction is based on applying Newton–Raphson iterations ...

In this paper an efficient numerical scheme to approximate the solutions of fifth-order boundary value problems in a finite domain with two different types of boundary conditions has been prsented, by taking basis functions with quartic Bsplines and weight functions with quintic B-splines in PetrovGalerkin method. In this method, the quartic B-splines and quintic B-splines are redefined into ne...

Three-dimensional curves are playing an increasing role in ship-hull modeling and many other areas of computer-aided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies currently pursued by CAD researchers: local fairing by knot removal, and local/global fairing based ...

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 ...

This paper proposes a dynamic path planning method based on discrete optimization applied to suburban highways or expressways. We optimize the generated candidate points according cost function and then generates local through quintic spline curve. The kinematics obstacle boundary conditions are set up improve reliability of planned path. Meanwhile, two-dimensional normal distribution function,...