Blind Parametric Interpolation Fitting For A Set Of Points

I have two vectors that together contain a set of points that define a contiuous shape that looks similar to, but is not the same as various common parametric curves. I want to (1) determine if there exists a parametric equaion that fits these points, and (2) if those equations exist, what are they? The shape is not, by definition, a cycloid or any other standard parametric shape, so I cannot start with an equation and simpily fit coefficients until the shapes match well. Is there a way to compute the parametric equations of a point set completely blind without first knowing the parent function? I only really care that part of the result is defined by the points, it wouldnt matter if the resulting parametric equations had loops inside the shape

Answer 1

[Matt J]

Is there a way to compute the parametric equations of a point set completely blind without first knowing the parent function?

No, but it's not clear why that would be necessary. You can always write the spline interpolation of your points as a parametric function:

pp = spline(t,[x(:),y(:)].');

xy=@(s) ppval(pp,s)  %parametric curve xy(s)

[Alex Treseder]

it would be for use in a desmos simulation. I figured this would probably not be possible to do, but wanted to check anyway. I have some clever work arounds to this problem. Thanks!

[Geoffrey Rivers]

@Matt J Do you mind reviewing this code for spline fit followed by parametric interpolation? I tried using this and I feel like it's missing a key step.

Does 't' need to be initialised prior to calling Spline, and if so, as what format does it need to be initialised? Sorry, function handles are a bit confusing to me, and I'm not clear on what's acceptable when it's being used for a spline interpolation, and how it fits in my workflow.

[Matt J]

Does 't' need to be initialised prior to calling Spline

In Matlab, all variables need to exist if they are to be passed to a function.