Beta-Bezier Curves

Bezier curves

i=0 aix , ai ∈ R. We will denote by πn the linear (vector) space of all such polynomials. The actual degree of p is the largest i for which ai is non-zero. The functions 1, x, . . . , x form a basis for πn, known as the monomial basis, and the dimension of the space πn is therefore n + 1. Bernstein polynomials are an alternative basis for πn, and are used to construct Bezier curves. The i-th Be...

5 Rational Bezier Curves Andrelief

Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

In this paper, we propose a method to obtain a constrained approximation of a rational Bézier curve by a polynomial Bézier curve. This problem is reformulated as an approximation problem between two polynomial Bézier curves based on weighted least-squares method, where weight functions ρ(t) = ω(t) and ρ(t) = ω(t) are studied respectively. The efficiency of the proposed method is tested using so...

Designing Modern Linkages to Trace Bezier Curves

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 ...

Quasi-Bezier curves integrating localised information

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...