Fast Generation of Bezier Curves and Anti-Aliasing.

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...

Reparametrization and Subdivision of Interval Bezier Curves

Interval Bezier curve are new representation forms of parametric curves. Using this new representation, the problem of lack of robustness in all state-of-the art CAD systems can be largely overcome. In this paper this concept has been discussed to form a new curve over rectangular domain such that its parameter varies in an arbitrary range , instead of standard parameter , -. Where and are real...

A Fast Anti-Aliasing Technique for Computer-Generated Images

We describe an efficient variation on the z-buffer algorithm for hidden-surface removal in computer-generated images, which allows to selectively post-filter such images in order to reduce the artifacts due to sub-sampling. With a moderate increase in both the computational cost and the memory needs of the classic z-buffer, we filter only those areas where aliasing is most noticeable and improv...