Bézier Curves and Control Points

There are various expressions for describing a shape, but the number of practical ones is limited. A polynomial expression in parametric form with control points is most useful in most applications, for it is not only mathematically simple, but also it has favorable properties for engineering design; its expression does not depend on coordinate systems, geometrical properties are easily grasped and manipulated by control points, unwanted waviness usually does not appear in construction and modification of shapes, and long curves and large areas can be designed by connecting short or small segments.