2008 Volume 21 Issue 2 Pages 60-68
We consider the problem of designing optimal smoothing spline curves by employing an approach based on linear control systems. First, the problem is formulated using continuous-time, time-invariant systems with piecewise constant inputs. Then by introducing discrete time-varying systems, the solutions for optimal splines including periodic splines are derived. The existence conditions for unique optimal solutions are established and linked to the concepts of controllability and observability. The computational procedures for the optimal splines are straightforward. The design method for periodic splines is applied to a shape synthesizing problem using jellyfish as the example.