Fit a spline function to a set of data points

Hi All,

I have a set of coordinate points

x= [0,4,6,10,15,20]

y = [18,17.5,13,12,8,10]

I want to fit a spline function.

Could someone please suggest the the curve fit function that can be used?

[Torsten]

Do you want to use spline interpolation or spline fitting ?

For spline fitting, use

https://de.mathworks.com/help/curvefit/spline-fitting.html

for spline interpolation, use "interp1" with the interpolation method "spline":

[Deepa Maheshvare]

Could you please also help me with the command that can do a linear interpolation between the datapoints (like what's seen in a line plot)?

[Sam Chak]

Okay, go to this 'interp1' documentation and use the 'spline' method.

Then see the example and post your code here. We will then try to fix it if there is an error.

[Deepa Maheshvare]

Hi,

Sorry for not updating here.

I tried

x = [0,4,6,10,15,20]

y = [18,17.5,13,12,8,10]

splinetool(x,y)

This is what I see for a cubic polynomial. I would also try to interpolate the values for a polynomial of degree 1 , linear interpolation. I couldn't find the option to set the polynomial degree here.

[Deepa Maheshvare]

Hi, Thanks . I get it, my mistake. `interp1` helps

[Deepa Maheshvare]

@Sam Chak,

x = [0,4,6,10,15,20]

y = [18,17.5,13,12,8,10]

vq = interp1(x,y,'linear')

returns NaN

[Deepa Maheshvare]

@Torsten,

I tried

x = [0,4,6,10,15,20]

v = [18,17.5,13,12,8,10]

vq = interp1(x,v, 'linear', 'pp')

xq = x

figure

vq1 = interp1(x,v,xq);

plot(x,v,'o',xq,vq1,':.');

title('(Default) Linear Interpolation');

returns

vq =

struct with fields:

form: 'pp'

breaks: [0 4 6 10 15 20]

coefs: [5×2 double]

pieces: 5

order: 2

dim: 1

orient: 'first'

Here I am not sure why the order (which I infer as the polynomial degree) is 2 for linear interpolation. Could you please explain this a bit?

Answer 1

[Sam Chak]

Hi @Deepa Maheshvare

Thought you want the 'spline'? Is there a reason to use the 'linear' method?

x   = [0, 4, 6, 10, 15, 20];
y   = [18, 17.5, 13, 12, 8, 10];
xq  = 0:0.01:20;

subplot(2,1,1)
yq1 = interp1(x, y, xq, 'linear');
plot(x, y, 'o', xq, yq1, '--');
ylim([5 22]), grid on, title('Linear Interpolation');

subplot(2,1,2)
yq2 = interp1(x, y, xq, 'spline');
plot(x, y, 'o', xq, yq2, '--');
ylim([5 22]), grid on, title('Spline Interpolation');

[Deepa Maheshvare]

@Sam Chak

Thank you, I wanted linear interpolation for a use case. `spline` is useful for me.

vq = interp1(x,v, 'linear', 'pp')

vq =

struct with fields:

form: 'pp'

breaks: [0 4 6 10 15 20]

coefs: [5×2 double]

pieces: 5

order: 2

dim: 1

orient: 'first'

Here I am not sure why the order (which I infer as the polynomial degree) is 2 for linear interpolation. Could you please explain this a bit?

[Torsten]

Seems that order = 2 means that two coefficients are needed to describe the (linear) spline function on each subinterval and is set to 1 + degree of the interpolating polynomial. A bit confusing in my opinion.

[Deepa Maheshvare]

@Torsten

Thanks a lot for the clarification.

Answer 2

[Simon Chan]

Use function spline