In this paper, the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is red...

This paper presents a new approach for fast and accurate generation of cubic spline trajectories for non-circular omnidirectional mobile robots and automated guided vehicles (AGVs). This method can be combined with any existing path planner or guidance system for offline calculation of trajectories with independent translational and rotational movement. In addition trough fast computation this ...

Both the 4-point and the uniform cubic B-spline subdivisions double the number of vertices of a closed-loop polygon P and produce sequences of vertices fj and bj respectively. We study the J-spline subdivision scheme Js, introduced by Maillot and Stam, which blends these two methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a family of limit curves, the ...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic Bsplines as weight functions has been developed to solve a general eighth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet, the N...

A finite element method involving collocation method with Quintic B-splines as basis functions has been developed to solve fifth order boundary value problems. The fifth order derivative for the dependent variable is approximated by the finite differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points se lected in ...

In our contribution we study cubic and quintic Pythagorean Hodograph (PH) curves in the Euclidean and Minkowski planes. We analyze their control polygons and give necessary and sufficient conditions for cubic and quintic curves to be PH. In the case of Euclidean cubics the conditions are known and we provide a new proof. For the case of Minkowski cubics we formulate and prove a new simple geome...

in many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, gis-based modeling approach was utilized to zoning pm2.5 dispersion over tehran, during one ye...

Surface offset is one of the most useful operations in Computer Aided Geometric Design (CAGD). However, an implementation of this operator is not trivial primarily because the offset surface, in general, does not have the same representation as the original surface. Hence, it is dif®cult or impossible to represent an exact offset in a system with limited surface forms. For this reason, some CAG...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and ...