Bezier curves on groups

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...

Selective Video Coding based on Bezier Curves

In this paper the problem of reconstruction of video frames is addressed, when there are missing pixels in each video frame or is corrupted with noise and also the locations of corrupted pixels are not known. The modified data can be corrected using Forward Error Correcting Codes. Forward Error correcting codes detect and correct errors with the help of complex decoders. This work proposes a ne...

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 ...