Fitting a polynomial curve to data points in two dimensions

Question

All packages I find to fit a polynomial are for one dimensional data. By that I mean the dependent variable is one dimensional. I have points with two dimensions on a plane. I know the order in time and I want to fit a cirve through it. It should be reasonably smooth. My intuition says it is a parametric curve of time but how to fit it ? perhaps some kind of spline or polynomial fit on plane? Equations of motion of a particle ?

Answer 1

One possible solution would be a parametric spline curve. This is a curve $\mathbf{S}(t) = \bigl(x(t),y(t)\bigr)$, where $t$ is some parameter, which in your case can be time.

These sorts of splines can be made to interpolate given data points at specified parameter values. In other words, given points $\mathbf{Q}_i$ and parameter values $t_i$, we can construct the curve $\mathbf{S}$ so that $\mathbf{S}(t_i) = \mathbf{Q}_i$ for all $i$.

Some further info and a reference in my answer to this question.

Also, my answer to this question.