Creating parametric equations using points

Question

I have points, x, y, and t, where t=1,...,Length[x]. I wished to make two parametric equation using the idea of interpolation, but not using the method in Mathematica. Any suggestion?

Answer 1

Let use BSpline interpolation. There is working example:

Preparadion of data:

t = Range[10];
x = t*Sin[t];
y = t*Cos[t];
pts = Transpose[{t, x, y}]

Plotting result

Graphics3D[{BSplineCurve[pts], Green, Line[pts], Red, Point[pts]}]