Composite Curves:
Let the problem of joining the curve segment
(u), (0 ≤ u ≤ 1) with the curve segment 
. Generally we would like to ensure continuity of the curve, its slope and even the curvature. Thus, we have the conditions
where t
is the common unit tangent and εi are parameters.
For curvature continuity, it specified
i.e.
This equation is satisfied by
here λ is an arbitrary scalar.