Bézierkõveraks

Bézierkõveraks is a type of parametric curve used in computer graphics and related fields. It is defined by a set of control points. The curve passes through the first and last control points, and the intermediate control points influence the shape of the curve by "pulling" it towards them. The degree of the Bézier curve is determined by the number of control points minus one. For example, three control points define a quadratic Bézier curve, and four control points define a cubic Bézier curve.

The mathematical definition of a Bézier curve involves Bernstein polynomials. For a set of n+1 control points P0, P1, ..., Pn, the Bézier curve B(t) is given by the formula B(t) = sum from i=0 to n of Bi,n(t) * Pi, where Bi,n(t) are the Bernstein basis polynomials and t is a parameter that ranges from 0 to 1. As t varies from 0 to 1, the point B(t) traces out the Bézier curve.

Bézier curves are widely used because of their intuitive control and smooth interpolation properties. They are particularly useful for defining smooth, flowing shapes in vector graphics editors, font design, and animation. Their ability to be easily manipulated by adjusting control points makes them a fundamental tool for creating and editing curves.