In CAGD applications, a curve may have a so complicated shape that it
cannot be represented by a single Bézier cubic curve since the shape
of a cubic curve is not rich enough
piecewise representation. A curve that is made of several Bézier
curves is called a composite Bézier curve or a Bézier
spline curve.
It is considerably involved to join Bézier curves with some order
of derivatives continuity
non-local effects caused by blending functions being non-zero for all
values of u
relationship between degree and number of points which means if need to
represent n points must use multiple segments or increase degree of curve
a composite Bézier curve requires more control vertices than a B-spline
curve