Bezier curve

Bezier curve refers to a family of polynomial used by French engineer [Pierre Bezier]? to design automobile bodies. The case with four control points is a cubic curve used in PostScript and other imaging systems.

Four points define a cubic Bezier curve. The curve starts from A going toward B and arrives at D coming from C.

    B o         o C
         _____
     _,-'     `-._
   ,'             `.
  /                 \ 
 * A               D *

The parametric form:

P(t) = A(1 - t)³ + 3Bt(1 - t)² + 3Ct²(1 - t) + Dt³

Notice a binomial pattern in the coefficients [1, 3, 3, 1]. Generalizing the cubic case forms the cases with more than four control points; however, these do not find much use in practice.

References

• http://astronomy.swin.edu.au/pbourke/curves/bezier/