Door passing is the basic capability of an intelligent wheelchair. This paper presents a novel approach to address the door passing issue using Bézier curve based path planning. The planed path consists of two segments: one from corridor to door and the other from door to the goal position. For each segment, an optimal Bézier curve is generated as a reference trajectory for an intelligent wheel...

A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous q...

In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along their geometric properties which are similar to the classical functions. A Bézier (ST-Bézier, curve and characteristics is also constructed. The continuity constraints connection adjacent ST-Bézier curves segments discussed. Shape control can provide ...

In [20] a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu [19] and Goldman [12], i.e., families that include both Bernstein and Lagrange polynomial, are generalized in a new way, (2) a...

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bézier curve segments. For a p...

This paper introduces a new approach for the fabrication of generalized developable cubic trigonometric Bézier (GDCT-Bézier) surfaces with shape parameters to address fundamental issue local surface adjustment. The GDCT-Bézier are made by means GDCT-Bézier-basis-function-based control planes and alter their modifying parameter value. designed maintaining classic characteristics when take on dif...

Two equations are presented which express the derivative of a rational Bézier curve in terms of its control points and weights. These equations are natural generalisations of the non-rational case and various properties are found from them. Bounds on the magnitude of the derivative and the direction of the derivative (the hodograph) are obtained. Expressions for the second derivative, curvature...

In this paper, we present a geometric construction of control meshes of helicoids over trapezium domain. We first introduce the quasi-Bézier basis in the space spanned by {1, t, cos t, sin t, t sin t, t cos t}, with t ∈ [0, α], α ∈ [0, 2π). We denote the curves expressed by the quasi-Bézier basis as algebraic-trigonometric Bézier curves, for short ATBézier curves. Then we find out the transform...

The presentation of Bézier surfaces affects the results of rendering and tessellating applications greatly. To achieve optimal parameterization, we present two reparameterization algorithms using linear Möbius transformations and quadratic transformations, respectively. The quadratic reparameterization algorithm can produce more satisfying results than the Möbius reparameterization algorithm wi...