Bezier curve with equation

C Graphics » Bezier curve with equation

Bezier curve was founded by a French scientist named Pierre Bézier. This Curve is drawn by using Control points. In this, Approximate tangents act as control points which are used to generate the desired Bezier. It is a parametric curve which follows bernstein polynomial as the basis function.

B(t) =  ∑ki=0  PkBkn(t)       , Where t lies between 0 and 1, 0<=t<=1

P represents number of control points

Bk, n(t)=  nCk    uk (1-t)n-k

Tangent: It is a straight line that exactly touches curve.

 

Types of Bezier Curve

1)  Simple Bezier Curve : The simple line connecting endpoint.

2) Quadric Bezier Curve: Quadric curve using 3 control points

3) Cubic Bezier Curve: Cubic curve using 4 control points

Properties:

1) A Bezier curve always depends on the number of control points that require to draw it.

2) Curve can be drawn using endpoints only.

3) The polynomial equation also depends on the number of control points Suppose, n is a control point than the degree of the polynomial equation will be n-1.

4) Curve passes through initial and terminating control points.

5) Closed Bezier curve can be generated by making first and last control points same.


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