Using Bezier curves in medical applications

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

Controlled Multi-Path Routing in Sensor Networks Using Bezier Curves

We address the problem of extending the lifetime of wireless sensor networks using multi-path routing based on a family of flexible routes with soft quality of service guarantees in terms of the packets’ delivery latency. We introduce a methodology based on Bezier curves as guiding trajectories in the routing process and we address the balancing of the workload among neighboring nodes. An added...

Fitting of Bezier Curves Using the Fireworks Algorithm

A swarm intelligence based method is presented in this paper to solve the problem of parameterization of given set of planar and spatial data points, which may be uniformly or non-uniformly spaced, for least squares fitting with Bezier curves. The basic framework of the proposed method relies on fireworks algorithm. Performance of the proposed method is tested through several example curves of ...

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...