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matlabinterpolationcurve

Interpolation between curves that may overlap

I try to interpolate curves in the gaps of some already existing curves using matlab (and the interp1-function).

Start of edit 1

I already have the data of 5 Torque over rpm curves that I obtained with a number of simulations for each curve. Since simulation time is precious, I would like to save time with the interpolation of curves that "fill the gap" between the already existing ones.

img

I'm looking to form the following:

img

Further thoughts of me down below.

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I tried to follow the steps from the question in the thread Interpolation between two curves (matlab) but it does not seem to work with my code. I am not sure if the code is actually applicable since the curves might overlap...

I tried to edit the code from the link above like the following:


% Save the data in one array each. The original data is stored in the
% arrays "x/yOriginal" row-wise.
curve1_data = [xOriginal(:,1) yOriginal(:,1)];
curve2_data = [xOriginal(:,2) yOriginal(:,2)];

% This was to try if the code from the link works
yy = [0:1:60];

xx1 = interp1(curve1_data(:,2),curve1_data(:,1),yy,'spline');
xx2 = interp1(curve2_data(:,2),curve2_data(:,1),yy,'spline');
m = 3; % Curve_Offset
mm(:,m) = xx1 + (xx2-xx1)*(m/(8750-5000));

% With the following I tried to interpolate over x
xx = (xOriginal(1,1):1:xOriginal(1,2));

yy1 = interp1(curve1_data(:,1),curve1_data(:,2),xx,'spline');
yy2 = interp1(curve2_data(:,1),curve2_data(:,2),xx,'spline');


m = 3; % Curve_Offset
% From the original code:
mm(:,m) = xx1 + (xx2-xx1)*(m/(8750-5000));

% Interpolation over x
yINT = yy1 + (yy2-yy1)*(m/8750-5000);

None of the interpolation-techniques worked, the y-values are either 90% negative (with the code from the link) or way too high (10e8 with the interpolation over x).

What I expected was that it creates a curve a little less steep than the curve "to its left" and a bit steeper than the curve "to its right".

My further thoughts:

The existing curves are the product of big 3-dimensional arrays. I.e. it could be that it is more the way to go to interpolate the arrays and then "read out" the Torque-over-rpm-Curves. On the other hand, I don't see a way to interpolate between two 1001-by-7001-by-5 arrays... Moreover, for the next steps with the programm, the curve-interpolation needs to be quite fine (it is necessary to have way more than 1 interpolated curve between two existing curves) which makes the problem even more difficult.

Solution

  • If I understand right, the plot is generated with something like this:

    plot(xOriginal(:,1),yOriginal(:,1))
plot(xOriginal(:,2),yOriginal(:,2))
% ...

    If so, you can plot an intermediate curve with

    plot((xOriginal(:,1) + xOriginal(:,2))/2, (yOriginal(:,1) + yOriginal(:,2))/2)

    That is, the average between each pair of coordinates forms a curve that is exactly half-way between the two original curves.

    Use weighted averages to generate more of these curves. This is linear interpolation.

    d = 0.2;
plot(d*xOriginal(:,1) + (1-d)*xOriginal(:,2), d*yOriginal(:,1) + (1-d)*yOriginal(:,2))

    Setting d = 0.5 we go back to the half-way case above.

    Example:

    xOriginal(:,1) = linspace(0.2,0.5,100);
yOriginal(:,1) = 3 * cos(xOriginal(:,1)*10-2.5) + 3;

xOriginal(:,2) = linspace(0.6,0.8,100);
yOriginal(:,2) = cos(xOriginal(:,2)*20-13.5) + 1;

clf; hold on
plot(xOriginal(:,1),yOriginal(:,1))
plot(xOriginal(:,2),yOriginal(:,2))

plot((xOriginal(:,1)+xOriginal(:,2))/2,(yOriginal(:,1)+yOriginal(:,2))/2)

    resulting plot

    (the interpolated line is in orange)