Use of interp2 in an arbitrary dataset (2024)

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Stathis Tingas am 27 Jan. 2024

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Bearbeitet: Stathis Tingas am 28 Jan. 2024

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Hello,

I would appreciate any help on the following issue.

I have a small dataset (3x3 matrix) which descirbes a mechanical property (say Z) in 2d space. Each line describes the mechanical property in the 2d space, hence I basically have 3 values of Z in the 2d space. Column 1 has the x-coordinate, column 2 has the y-coordinate and column 3 the respective value for Z.

For the sake of an example, my data looks like this:

X Y Z

0.25 0.25 0.5

0.50 0.60 1.5

0.75 0.35 3.0

I want to interpolate (between the given values) and extrapolate (from 0 up to 1 for both X and Y), ideally using spline, cubic or makima.

My plan was to use the following code:

x=[0.25;0.50;0.75];

y=[0.25;0.60;0.35];

[X,Y] = meshgrid(x,y);

Z = [0.5; 1.5; 3.0];

[Xq,Yq] = meshgrid(0:.01:1, 0:.01:1);

Zq = interp2(X,Y,Z,Xq,Yq,'spline');

However, when I try that, I get the following error:

Error using griddedInterpolant

Interpolation requires at least two sample points for each grid dimension.

Error in interp2>makegriddedinterp (line 226)

F = griddedInterpolant(varargin{:});

Error in interp2 (line 134)

F = makegriddedinterp(X, Y, V, method,extrap);

Could anyone advise?

Thanks

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Walter Roberson am 27 Jan. 2024

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x=[0.25;0.50;0.75];

y=[0.25;0.60;0.35];

Z = [0.5; 1.5; 3.0];

[Xq,Yq] = meshgrid(0:.01:1, 0:.01:1);

F = scatteredInterpolant(x, y, Z);

Zq = F(Xq, Yq);

surf(Xq, Yq, Zq)

Use of interp2 in an arbitrary dataset (3)

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Stathis Tingas am 27 Jan. 2024

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Bearbeitet: Stathis Tingas am 28 Jan. 2024

Dear @Walter Roberson

Thank you for your response but to my understanding, scatteredInterpolant does not allow the use of spline, cubic or makima functions? Am I right? If so, is there a workaround to use particularly spline or makima?

Thanks

Stathis

William Rose am 27 Jan. 2024

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@Stathis Tingas,

You have 3 data points, on a 2D surface. That is the minimum number needed to define a plane (assuming they are not collinear). With so few points, you cannot estimate a more sophisticated surface, such as a spline. You would need at least 4 points (2 in each dimension) to use makima and at least 16 (4 in each dimension) to use spline. With only three points, linear interpolation is your only option.

Stathis Tingas am 27 Jan. 2024

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Bearbeitet: Stathis Tingas am 28 Jan. 2024

Thank you @William Rose for your response. I wasnt actually aware of this requirement for spline and makima.

My dataset will generally be small but it will vary from 3 up to 11-12 points. You are saying that makima would need 4 points. Therefore, if the original dataset as an example has the following 4 points, how could I use makima or cubic?

x=[0.25;0.50;0.75;0.9];

y=[0.25;0.60;0.35; 0.7];

Z = [0.5; 1.5; 3.0; 3.5];

Thanks

Torsten am 27 Jan. 2024

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Bearbeitet: Torsten am 27 Jan. 2024

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If your data are not gridded, you will have to live with "ScatteredInterpolant" and its interpolation methods.

And your four points in 2d constitute a curve. So Z could be interpolated on this curve maybe, but it makes little sense to treat them as sufficient to interpolate on a real two-dimensional rectangle.

x=[0.25;0.50;0.75;0.9];

y=[0.25;0.60;0.35; 0.7];

Z = [0.5; 1.5; 3.0; 3.5];

plot3(x,y,Z)

grid on

Use of interp2 in an arbitrary dataset (8)

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Sulaymon Eshkabilov am 27 Jan. 2024

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Is this what you wanted to obtain:

% Given DATA:

Data = [ 0.25 0.25 0.5;

0.50 0.60 1.5;

0.75 0.75 3.0];

% Extract x, y, and z from Data

x = Data(:, 1);

y = Data(:, 2);

z = Data(:, 3);

[X,Y]=meshgrid(x,y);

Z = meshgrid(z);

% Interpolate using griddata

[Xq,Yq] = meshgrid(0:.01:1);

Zq = interp2(X,Y,Z,Xq,Yq,'spline');

% Plot the results

figure;

scatter3(x, y, z, 'ro', 'filled'); % Original data points in red

hold on;

surf(Xq, Yq, Zq, 'EdgeColor', 'none', 'FaceAlpha', 0.5); % Interpolated/extrapolated surface

xlabel('X');

ylabel('Y');

zlabel('Z(X,Y)');

title('Interpolation and Extrapolation of Mechanical Property');

Use of interp2 in an arbitrary dataset (10)

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Torsten am 27 Jan. 2024

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Bearbeitet: Torsten am 27 Jan. 2024

@Sulaymon Eshkabilov

You already interpolate (extrapolate) when you assume that (x,y,z) can be extended to (X,Y,Z) as existing database for interpolation with interp2.

Stathis Tingas am 27 Jan. 2024

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Bearbeitet: Stathis Tingas am 27 Jan. 2024

Dear @Sulaymon Eshkabilov, thanks for your response which seems to work fine but you have made a mistake in your Data matrix and this seems to make a difference.

In particular, the 3rd element in the y vector should be 0.35 and not 0.75.

When I try to use 0.35 with your version of the code, I get:

Error using griddedInterpolant

Sample points must be sorted in ascending order.

Error in interp2>makegriddedinterp (line 226)

F = griddedInterpolant(varargin{:});

Error in interp2 (line 134)

F = makegriddedinterp(X, Y, V, method,extrap);

Is there a workaround for this error?

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Translated by Use of interp2 in an arbitrary dataset (13)

Use of interp2 in an arbitrary dataset (14)

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Use of interp2 in an arbitrary dataset (2024)

FAQs

How does interp2 work? ›

The interp2 command interpolates between data points. It finds values of a two-dimensional function underlying the data at intermediate points. Interpolation is the same operation as table lookup.

What is the use of interp1 function in Matlab? ›

Description. vq = interp1( x , v , xq ) returns interpolated values of a 1-D function at specific query points using linear interpolation. Vector x contains the sample points, and v contains the corresponding values, v(x). Vector xq contains the coordinates of the query points.

What is interpolation in 2 dimensions? ›

Two dimensional interpolation takes a series of (x,y,z) points and generates estimated values for z's at new (x,y) points. Interpolation is used when the function that generated the original (x,y,z) points is unknown. Interpolation is related to, but distinct from, fitting a function to a series of points.

How does image interpolation work? ›

The basic idea of interpolation is quite simple: first, reconstruct a “continuous” image from the discrete input image, then sample this “continuous” image onto the grid of the output image. Interpolation methods differ from the way the “continuous” image is reconstructed.

What is an example of interpolation? ›

Interpolation definition says that interpolation is to estimate the value of a point between two given points in a data set. For example, if a child's height was measured at age 5 and age 6, interpolation could be used to estimate the child's height at age 5.5.

How to interpolate data? ›

How to interpolate
  1. Organize your data. First, put the data you've collected into a chart that shows your independent and dependent variables. ...
  2. Consider creating a graph. ...
  3. Select your two points. ...
  4. Enter values into the interpolation equation. ...
  5. Solve for the missing variable.
Oct 16, 2023

Does interp1 extrapolate? ›

yi = interp1(x,Y,xi,method,'extrap') uses the specified method to perform extrapolation for out of range values. yi = interp1(x,Y,xi,method,extrapval) returns the scalar extrapval for out of range values. NaN and 0 are often used for extrapval . The interp1 command interpolates between data points.

How does motion interpolation work? ›

Motion interpolation or motion-compensated frame interpolation (MCFI) is a form of video processing in which intermediate film, video or animation frames are generated between existing ones by means of interpolation, in an attempt to make animation more fluid, to compensate for display motion blur, and for fake slow ...

How does string interpolation work? ›

In computer programming, string interpolation (or variable interpolation, variable substitution, or variable expansion) is the process of evaluating a string literal containing one or more placeholders, yielding a result in which the placeholders are replaced with their corresponding values.

How does spline interpolation work? ›

That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-nine polynomial to all of ...

How does bilinear interpolation work? ›

The bilinear interpolation process uses the average of the data at each corner of the rectangle. The weights are based on the separation between the point and the corners for a (x,y) position inside the rectangle. The weight of the corner increases the closer it is to the tip.

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