A design of a class of linkages is presented which are less complex than those suggested by Kapovich and Millson in the con…guration of conventional planar linkages. Conventional linkage constraints are relaxed allowing sliding joints and telescoping links. The precise number of …xed links, telescoping links, and sliding contacts is determined for this modern linkage to trace a Bézier curve of ...

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product patches. Our results rely on using te...

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...

In this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. Our results generalize the corresponding results obtained by Y. J. Cho, R. Saadati, Shenghua Wang (Y. J. Cho, R. Saadati, Shenghua Wang, Common fixed point  heorems on generalized distance in ordere...