Rational Bezier and B-spline representations of circles have been heavily publicized. However, all the literature assumes the rational Bezier segments in the homogeneous space are both planar and (equivalent to) quadratic. This creates the illusion that circles can only be achieved by planar and quadratic curves. In this paper we show circles that are formed by higher order rational Bezier curv...

-In this paper, we will present a simple and quick sampling method to digitize the cubic Bezier curves via controlled the chordal error. Key-Words: sampling method, chordal error, cubic Bezier curve

In this paper, the smooth path planning problem is considered for a mobile robot based on the genetic algorithm and the Bezier curve. The workspace of a mobile robot is described by a new grid-based representation (2 × 2n grids) that facilitates the operations of the adopted genetic algorithm. The chromosome of the genetic algorithm is composed of a sequence of binary numbered grids (i.e., cont...

in the present paper, the deformation zone of the ecae (equal channel angular extrusion) process was investigated using the upper bound theorem. for this purpose, the shape of the streamlines in the deformation zone was assumed to be cubic bezier curves. then, the force required for the ecae process was optimized with regard to the parameters defining the shape of streamlines by the upper bound...

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 presents a new method to generate curves, which allows the designer to produce a curve in combinational way allowing him to get the shape that he had in his imagination with keeping the four control point for the curve design. Basing on the modified BEZIER curve, the upgraded algorithm used de Casteljau algorithm on interval [r, s] as a mathematical base to upgrade the suggested meth...

Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading t...