What Is Bézier Curve

Q

What Is Bézier Curve?

✍: FYIcenter.com

A

Bézier Curve, named after Pierre Bézier, is related to Bernstein polynomial and widely used in computer graphics.

The Bézier Curve Bp0p1...pn(t) for a given set of n+1 points p0, p1, ..., pn with t=(0,1) can be defined in the following recursive form:

Bp0(t) = p0, t=(0, 1)
Bp0p1...pn(t) = (1-t)Bp0...pn-1 + tBp1...pn, t=(0, 1)

Graphically, a 2-point Bézier Curve Bp0p1(t) can be presented as:

Bézier Curve of 2 Points
Bézier Curve of 2 Points

Graphically, a 3-point Bézier Curve Bp0p1p2(t) can be presented as:

Bézier Curve of 3 Points
Bézier Curve of 3 Points

Graphically, a 4-point Bézier Curve Bp0p1p2p3(t) can be presented as:

Bézier Curve of 4 Points
Bézier Curve of 4 Points

 

Draw 3-Point Bézier Curve in OpenOffice

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2021-10-10, 184👍, 0💬