Bezierkõverateks

Bézier curves are parametric curves used in computer graphics and related fields to model smooth curves. They are defined by a set of control points, where the first and last control points are typically the endpoints of the curve. The intermediate control points influence the shape of the curve by "pulling" it towards them. A Bézier curve is always contained within the convex hull of its control points.

The mathematical definition of a Bézier curve relies on Bernstein polynomials. For a curve with n+1 control points P0, P1, ..., Pn, the curve B(t) is defined for t ranging from 0 to 1. The formula involves a sum of each control point multiplied by a Bernstein basis polynomial of degree n, evaluated at t. As t varies from 0 to 1, B(t) traces the curve from P0 to Pn.

Bézier curves are widely used in vector graphics software, such as Adobe Illustrator and Inkscape, for drawing and manipulating shapes. They are also employed in font design, animation, and robotics. The degree of the Bézier curve is determined by the number of control points minus one. Cubic Bézier curves, with four control points, are particularly common due to their versatility and intuitive control. Quadratic Bézier curves, with three control points, are simpler and can be efficiently rendered. Higher-degree Bézier curves can represent more complex shapes but can also be computationally more expensive.