This paper presents a path planning method considering physical limits for two-wheeled mobile robots (TMRs). A convolution operator is used to generate the center velocity trajectory to travel the distance along predefined Bezier curve while considering the physical limits. The trajectory gained through convolution does not consider the rotating angle of TMR, so we present a transformational me...

This paper proposes four methods to approximate circular arcs using quartic Bezier curves. Barycentric coordinates of two/three combination of control points are used to obtain an optimal approximation. Interior control points of quartic Bezier curves are found by satisfying G data from given circular arcs. The maximum errors between circular arcs and approximated curves are calculated using Ha...

This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch, computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the ...

Parametric-surface tessellation is one of the most important algorithms for CAGD applications. This paper presents a new parametric-surface tessellation method based on degree reduction: (1) a given parametric surface (or NURBS surface) of degrees (p; q) is decomposed into a set of Bezier surfaces, (2) the Bezier surfaces are converted into a set of bilinear surfaces by applying consecutive ste...

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

A four-parameter family of multivariable big q-Jacobi polynomials and a threeparameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable polynomials. A link is made between the orthogonality measures and R. Askey’s q-extensions of Sel...

In this paper we introduce a family of two-variable derivative polynomials for tangent and secant. Generating functions for the coefficients of this family of polynomials are studied. In particular, we establish a connection between these generating functions and Eulerian polynomials.

We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials.

The paper presents a method of expressing CST shapes pioneered by Kulfan into stan­ dard Bezier curves and surfaces. Out of the seven standard shape classes identified by Kulfan as representable using CST curves, four of them, including airfoils, can be repre­ sented as Bezier curves exactly. For the other three, a convergent series expansion proves insufficient to achieve any practical accurac...

In this paper, we study the spatial node stationary distribution of two variations of the Random Waypoint (in short, RWP) mobility model. In particular, differently from the RWP mobility model, that connects source to destination points by straight lines, our models make use of Manhattan or (more realistically) Bezier paths. We provide analytical results for the spatial node stationary distribu...