Recursively determine cubic spline coefficients

Question

I am looking for a way to fit a cubic spline on previously recorded points without using matrices. The software is running on an embedded microcontroller which is low on RAM, so calculating my coefficients (at least 18points, double precision) the way it is described here or here is probably not feasible. Is there a way to determine the coefficients recursively (e.g. segment by segment), so that I can avoid inverting 68x68 matrix (for 18pts/17 segments)?

Answer 1

You can use centripetal Catmull-Rom spline to create the spline that interpolate all the data points without matrix inversion.