Cubic spline or polynomial interpolation of non strictly increasing x in Scilab

Question

I have a set of xy points:

x = [1 2 3 3 2]
y = [1 1 2 3 2]

plot of the points

I would like to do an interpolation of those point. My issue is, interp1() or splin() require a strictly ecreasing x.

How can I get an interpolation like this:

x = [1 2 3 4 5]
y = [1 1 2 3 2]
xx = linspace(1, 5, 100);
yy2 = interp1(x, y, xx, 'spline');
plot(xx',yy2)
scatter(x, y)

interp1 interpolation plot

But with a non increasing x ?

I do not only need the plot, but also get the interpolation value for a given x and y.

You have duplicate values of x with different y value. Do you want to approximate you data in the least square sense ? — Stéphane Mottelet, Mar 09 '21 at 14:02

Stéphane Mottelet · Accepted Answer · 2021-03-09T15:24:48.720

1

This is a parametric curve, you have to consider a third vector t (the values of the parameter) and compute two splines. You can change the spline type by changing the third parameter (see the splin help page):

x = [1 2 3 3 2];
y = [1 1 2 3 2];
t = 1:5;
dx = splin(t,x,"natural");
dy = splin(t,x,"natural");
tt=linspace(t(1),t($),1000);
plot(interp(tt,t,x,dx),interp(tt,t,y,dy),x,y,'o')

edited Mar 09 '21 at 15:24

answered Mar 09 '21 at 14:11

Stéphane Mottelet

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Cubic spline or polynomial interpolation of non strictly increasing x in Scilab

1 Answers1