Bézieri

Bézieri is a type of parametric curve used in computer graphics and related fields. It is named after the French engineer Pierre Bézier, who used it in the 1960s for designing automobile bodies. The Bézier curve is defined by a set of control points. The shape of the curve is determined by the number and position of these control points. The curve starts at the first control point and ends at the last control point, but does not generally pass through any of the other control points. Instead, the curve is tangent to the line segment connecting the first two control points at the first point, and tangent to the line segment connecting the last two control points at the last point. This property makes Bézier curves useful for smooth, precise control of shapes. Bézier curves are widely used in computer-aided design (CAD), computer graphics, and animation. They are also used in font design, where they allow for the creation of smooth, flowing letters. The mathematical representation of a Bézier curve is given by the Bézier formula, which is a linear combination of the control points, weighted by binomial coefficients. This formula allows for efficient computation of the curve's points.