MATLAB: Interpolating curve with tangent ends

curveinterpolationtangent ends

Hello, I need to construct interpolating curve from data points (I have 3 points in plane) with tangent ends. I know derivative at the ends (in points 1 and 3). Could anybody advise how to do it?

Thanks, Michal

Best Answer

Hi Michal,

depending on the data, the spline function could give good results. see help spline, where it says that if Y contains two more values than X has entries, then the first and last value in Y are used as the endslopes for the cubic spline.

Related Solutions

MATLAB: Interpolation method (spline)

From the documentation:

'spline':

‘Spline interpolation using not-a-knot end conditions. The interpolated value at a query point is based on a cubic interpolation of the values at neighboring grid points in each respective dimension.’

It does not appear to be the same as 'cubic'. According to the documentation, 'cubic' is currently the same as 'pchip'.

MATLAB: Tangent

You'll need to fit a function to the data and then take its derivative. First, the fit:

plot(x,y,'.'); hold on
n = 10;
[p,~,mu] = polyfit(x,y,n); % degree 10 polynomial fit, centered and scaled
% Plot the fit with the data
xfit = linspace(min(x),max(x),100);
yfit = polyval(p,xfit,[],mu);
plot(xfit,yfit,'r')

Now you can use a numerical derivative to calculate the tangent. I recommend downloading the package Adaptive Robust Numerical Differentiation package from the File Exchange. Then you can do the following:

idx = input(['Enter index in the range ',num2str([1 length(x)]),':']);
x0 = x(idx);
f = @(x) polyval(p,x,[],mu);
df = derivest(f,x0); % Here is the derivative
% Calculate the end points of a tangent line
xt = [x0-0.05 x0+0.05];
yt = f(x0) + (xt-x0)*df;
plot(xt,yt)

(Edited to accept an index number instead of an x value).

Best Answer

Related Solutions

MATLAB: Interpolation method (spline)

MATLAB: Tangent

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