Lets say I have a set of coordinates which when correctly (directly - a straight line) connected form a shape (a simple curve if you will). Think of star-shape, important is that a xalue x might have 1 or more corresponding y-values.
Task is to interpolate the given dataset with a cubic-spline interpolation.
Now with a for a a set of points where we have $\forall y_i : y_i \neq y_j $ this is trivial, I can just create my splines and be done with it.
How can I do this with the given points ?
If you need I can post the points in question.
Points are as follows (prepare to be spooked):
x | y
13.0 0.0
11.5 0.0
10.0 2.0
11.0 4.0
9.0 5.5
6.0 6.0
0.0 5.0
6.0 7.0
10.5 7.0
13.0 7.5
15.0 7.0
15.0 9.0
16.0 10.0
19.0 9.0
17.0 8.5
16.5 8.0
16.0 7.0
15.0 6.0
15.0 4.5
15.5 3.5
14.5 2.5
15.0 3.5
14.0 4.5
13.0 4.5
12.0 2.5
11.0 1.5
13.0 0.0