Bézier curve
A Bézier curve is a type of parametric curve (a curve defined by a set of equations changing in respect to another variable) that is used in computer graphics and related fields. It is used to define curves of very specific shapes. Such curves can be adjusted to become curvier or straighter depending on the geometric shape (such as a triangle) used to create the curve.
In computer science, they are used to make specific curve shapes. In programs such as Adobe Illustrator or Microsoft PowerPoint, increasing the line symbol of a curve will increase the curviness of the curve.
Bézier Curve Media
Cubic Bézier curve with four control points
The basis functions on the range t in [0,1] for cubic Bézier curves:*blue: y = (1 − t)3,*green: y = 3(1 − t)2t,*red: y = 3(1 − t)t2, and*cyan: y = t3.
Quadratic Béziers in string art: The end points (•) and control point (×) define the quadratic Bézier curve (⋯).
A cubic Bézier curve (yellow) can be made identical to a quadratic one (black) by*1. copying the end points, and*2. placing its 2 middle control points (yellow circles) 2/3 along line segments from the end points to the quadratic curve's middle control point (black rectangle).
Equivalence of a quadratic Bézier curve and a parabolic segment
Animation of a linear Bézier curve, t in [0,1]
Construction of a quadratic Bézier curve
Construction of a cubic Bézier curve
Animation of a cubic Bézier curve, t in [0,1]
