Bézier Curve

Bézier Curve

Bézier Curve is a parametric curve used in computer graphics and related fields to model smooth curves that can be scaled indefinitely. Bézier curves are widely used in vector graphic design, animation, and computer-aided design (CAD) to create smooth, precise curves and surfaces. Named after French engineer Pierre Bézier, who developed the mathematical formula in the 1960s for use in automotive design, Bézier curves are defined by a set of control points that determine the shape of the curve. The curve is formed by a polynomial function that interpolates between these control points, resulting in a smooth, continuous curve that passes through the first and last control points and is tangent to the line segments connecting the control points. The degree of the Bézier curve is determined by the number of control points minus one. Quadratic Bézier curves have three control points and are the simplest type, while cubic Bézier curves, with four control points, are the most commonly used in graphic design applications. Higher degree curves are possible but less common. Bézier curves can be combined to create complex shapes and are infinitely scalable without losing their smoothness. They are computationally efficient to generate and manipulate, making them a fundamental tool in vector graphics and computer-aided design. Interestingly, while working on the Bézier curve, Pierre Bézier used a physical contraption made of wood and metal to visualize the curve, which resembled a large number of weights on a wire.

vector graphics, computer-aided design, animation, graphic design, parametric curves, control points

— Stephan Trump

CITATION : "Stephan Trump. 'Bézier Curve.' Design+Encyclopedia. https://design-encyclopedia.com/define/b%C3%A9zier-curve?E=435944 (Accessed on October 14, 2026)"