Dear sir.
I have developed my custom 2D&3D CAD/CAM soft for designing and manufacturing free curve and surface in the past.
I have integrated my soft mentioned above with AutoCAD , I have converted AutoCAD to 2D&3D CAD/CAM system.
I am sure that I can finish your proposal.
But I have several doubts.
firstly. there are several formats for free curve.
e.g. spline curve, B-spline curve, NURBS curve.
I think you proposal is 3 degree spline curve.
secondly, what is the dimension of your curve?
I think the dimension is 2D.
By my experience, to get closed free curve you must solve special linear system.
coefficient matrix has special type.
To adapt universal gauss method or gauss-zaide method is not proper for this. and memory is consumed.
I have already developed the my method to avoid this problem.
if you like me, please send me your response.
and I like skype. my skype ID is mosember.
best regards.
xinghai