Help with making an Ellipse Area function

I am having trouble making my ellipse function work. I am using X,Y data in the function although there is an error in the script that is not allowing me to find the area. Also I would love help on displaying the ellipse.

This is the code for my function.

function[area] = Ellipse_Area(FCOPX,FCOPY)
sFCOPX=FCOPX*1000;
sFCOPY=FCOPY*1000;
Sx = std(sFCOPX);
Sy = std(sFCOPY);
Syx = 0;
for i = 1:length(sFCOPX)
    Syx = Syx + (sFCOPX(i) - mean(sFCOPY))*(sFCOPX(i) - mean(sFCOPX));
end

[Walter Roberson]

Syx = Syx + (sFCOPX(i) - mean(sFCOPY))*(sFCOPX(i) - mean(sFCOPX));

Each time through the loop, mean(sFCOPY) and mean(sFCOPX) are going to be the same as on the other iterations, as neither sFCOPY nor sFCOPX are changing. It would therefore make more sense to assign the mean() to variables before the loop and use the variables inside the loop.

mean_sFCOPY = mean(sFCOPY);
mean_sFCOPX = mean(sFCOPX);
for i = 1:length(sFCOPX)
    Syx = Syx + (sFCOPX(i) - meansFCOPY)*(sFCOPX(i) - mean_sFCOPX);
end

Answer 1

[prabhat kumar sharma]

Hello Brendan,

To calculate the area of an ellipse using your X and Y data, you can follow these steps:

1. Scale the Data: As you've done, scale your X and Y data if needed.
2. Calculate the Covariance Matrix: Use the covariance of your data to find the semi-major and semi-minor axes of the ellipse.
3. Calculate the Area: The area of an ellipse is given by (\pi \times a \times b), where (a) and (b) are the lengths of the semi-major and semi-minor axes.

Here's a MATLAB function to calculate the area and display the ellipse using dummy data:

FCOPX = randn(100, 1);
FCOPY = randn(100, 1);
Ellipse_Area(FCOPX, FCOPY);
function [area] = Ellipse_Area(FCOPX, FCOPY)
    % Scale the data
    sFCOPX = FCOPX * 1000;
    sFCOPY = FCOPY * 1000;

    % Calculate the covariance matrix
    covMatrix = cov(sFCOPX, sFCOPY);

    % Eigen decomposition to find the axes
    [eigenVecs, eigenVals] = eig(covMatrix);

    % Semi-major and semi-minor axes
    a = sqrt(max(diag(eigenVals)));
    b = sqrt(min(diag(eigenVals)));

    % Calculate the area of the ellipse
    area = pi * a * b;

    % Display the ellipse
    theta = linspace(0, 2*pi, 100);
    ellipseX = a * cos(theta);
    ellipseY = b * sin(theta);

    % Rotate the ellipse
    phi = atan2(eigenVecs(2, 1), eigenVecs(1, 1));
    R = [cos(phi), -sin(phi); sin(phi), cos(phi)];
    ellipse = R * [ellipseX; ellipseY];

    % Plot the ellipse
    figure;
    plot(sFCOPX, sFCOPY, 'b.', 'DisplayName', 'Data Points');
    hold on;
    plot(mean(sFCOPX) + ellipse(1, :), mean(sFCOPY) + ellipse(2, :), 'r-', 'LineWidth', 2, 'DisplayName', 'Fitted Ellipse');
    xlabel('Scaled X');
    ylabel('Scaled Y');
    title('Ellipse Fitting');
    legend;
    axis equal;
    grid on;

    % Display the calculated area
    fprintf('The area of the ellipse is: %.2f square units\n', area);
end

I hope it helps!

[Brendan]

Thank you

Answer 2

[Star Strider]

The only error I can see is that you need to assign something to the ‘area’ variable in your ‘EllipseArea’ function.

I assigned ‘Syx’ to it here —

x = rand(5,1)

x = 5×1

0.3437 0.3771 0.6304 0.4375 0.7183

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y = rand(5,1)

y = 5×1

0.7692 0.5958 0.9679 0.3846 0.2130

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A = Ellipse_Area(x, y)

A = 1.0808e+05

function [area] = Ellipse_Area(FCOPX,FCOPY)
sFCOPX=FCOPX*1000;
sFCOPY=FCOPY*1000;
Sx = std(sFCOPX);
Sy = std(sFCOPY);
Syx = 0;
for i = 1:length(sFCOPX)
    Syx = Syx + (sFCOPX(i) - mean(sFCOPY))*(sFCOPX(i) - mean(sFCOPX));
end
area = Syx;
end

.

[Brendan]

Thank you

[Star Strider]

My pleasure!