Based on the technique of C-shape G Hermite interpolation by cubic Pythagorean-Hodograph (PH) curve, we present a simple method for Cshape G Hermite interpolation by rational cubic Bézier curve. The method reproduces a circular arc when the input data come from it. Both the Bézier control points, which have the well understood geometrical meaning, and the weights of the resulting rational cubic...

We construct the Stancu-type generalization of q-Bernstein operators involving idea Bézier bases depending on shape parameter ?1???1 and obtain auxiliary lemmas. discuss local approximation results in term a Lipschitz-type function based two parameters maximal function, as well other related for our newly constructed operators. Moreover, we determine rate convergence by means Peetre’s K-functio...

We propose the extended Bézier spiral in this paper. The spiral is useful for both design purposes and improved aesthetics. This is because the spiral is one of the Bézier curves, which play an important role in interactive curve design, and because the assessment of the curve is based on the human reception of the curve. For the latter purpose we utilize the logarithmic distribution graph that...

In this paper a computationally effective trajectory generation algorithm of mobile robots is proposed. The algorithm plans a reference path based on Voronoi diagram and Bézier curves, that meet obstacle avoidance criteria. Bézier curves defining the path are created such that the circumference convex polygon of their control points miss all obstacles. To give smoothness, they are connected und...

We classify mutual position of a quadratic Bézier curve and a regular quadric in three dimensional Euclidean space. For given first and last control point, we find the set of all quadratic Bézier curves having no common point with a regular quadric. This system of such quadratic Bézier curves is represented by the set of their admissible middle control points. The spatial problem is reduced to ...

An explicit expression for the unique implicitization of any planar rational cubic Bézier curve is presented, the only exception being when the tangents at the ends of the curve are parallel. The representation is in the form of a cubic Bernstein-Bézier triangle and is invariant under affine transformations of the curve. The implicitization degenerates to zero if and only if the curve degenerat...

2. MAIN RESULTS In this paper, subdivision methods for rectangular Bézier A rectangular Bézier surface of degree n 3 m can be surfaces are generalized to subdivide a rectangular Bézier surface patch of degree n 3 m into two rectangular Bézier surrepresented by face patches of degree n 3 (m 1 n), while the parameter domain of the Bézier surface is decomposed into two trapezoids. As an applicatio...

When designers begin a product design, they create their ideas and expand them. This process is performed on paper, and designers’ hand-drawn lines are called sketches. If the designers’ hand-drawn sketches can be realized as real curves, it would be effective in shortening the design period. We have developed a method to extract five degree Bézier curves based on a hand-drawn sketch. The basic...

This paper presents a geometric interpolation method for curve approximation in 3 R space. Given a curve, the new method is to find an approximation Bézier curve of degree 4 tangent with the given curve at the two end points and at an inner point as well. The resulting Bézier curve is explicitly expressed in the parameters of the tangent inner point of both the given curve and the approximation...

Approximating a hand-written curve by a Bézier curve can be performed by two main processes: (1) the selection of the significant points on the curve and (2) the curve approximation. This paper focuses on finding a set of featured points, which is an important component for curve fitting into a Bézier curve. This new approach is an extension of the authors’ previous work by reducing the weaknes...