How to plot and curve through N points and find coordinates of K points from curve plotted (N<<<K)

I am new to MATLAB. i wish to plot a curve through N points(N=7). Later from the curve plotted i wish to extract coordinates of K points (K=50). I did find some interpolation codes for curve passing through points. For 7 points we need a polynomial of degree 6. I find it to be complicated and st time curve does not match as needed. Will spline curve do?

Answer 1

[Walter Roberson]

coeffs = polyfit(x, y, 6);
newx = linspace(min(x), max(x), 50);
newy = polyval(coeffs, newx);

Will spline curve do? Probably not. But it will depend upon your data and upon the region where you need to interpolate and upon your meaning of "do".

[guru85]

From what i read splines can be interpolated piecewise hence give better approximation of curve compared to a curve interpolated by Lagrange. Also for Lagrange higher the points higher is the data.

[Walter Roberson]

spline curves correspond to bending a stiff material to touch particular points. If that is not what you are modeling, then a spline fit is not going to give you an accurate approximation. It might well give you a visually pleasing curve, but not an accurate one.

To get an accurate approximation you need to know the mathematical form of the process that generated the data.

[guru85]

x  =[0  5  10  15  20  25  30  35]
y  =[0.1256  0.1096  0.1221  0.0732  0.0878  0.1216  0.135  0.139]

These are the point coordinates (x,y). now i want a curve to pass to all these points. These are error data of a surface edge. as you can see it is not straight line but slightly bent /curved. i want to interpolate a curve through these points.

[guru85]

after i fit a curve through these point. i need to extract as many as possible (x,y) coordinate points (say 80 points) from the curve

[Walter Roberson]

[coeffs, s, mu] = polyfit(x, y, length(x));
newx = linspace(min(x), max(x), 80);
newy = polyval(coeffs, newx, s, mu);
newys = interp1(x,y,newx,'spline');
plot(x,y,'b', newx, newy, 'r', newx, newys, 'k')

However, remember that the fact that the spline is "closer" to the original points does not mean that the spline is any more accurate. What you need is either more (x,y) points or else a theoretical formula relating x and y that could be used to predict points.

[guru85]

thank you. since data is limited, i think i will predict in-between data using ANN. If i have any doubts i will contact you sir. thank you.

[Walter Roberson]

GIGO