What is Bezier curve?

A Bézier curve is a parametric curve frequently used in computer graphics, animation, and modeling to create smooth and scalable shapes. It is defined by a set of control points, which determine its shape. The curve is mathematically represented using Bernstein polynomials and is widely used because it provides excellent control and precision.

Control points

A bezier curve is defined by control points.

There may be 2, 3, 4 or more.

For instance, two points curve:

Three points curve:

Four points curve:

Key Characteristics

1. Control Points:
   • The curve starts at the first control point (P0P_0P0​) and ends at the last control point (PnP_nPn​).
   • The other control points (P1,P2,…P_1, P_2, \ldotsP1​,P2​,…) influence the shape but are not necessarily on the curve.
2. Tangency:
   • The curve’s tangent at the endpoints aligns with the line connecting the endpoint to its adjacent control point.
3. Convex Hull:
   • The curve always lies within the convex hull of its control points.
4. Scalability and Transformability:
   • Bézier curves scale and transform well, making them ideal for vector graphics.