Cone fitting in Matlab

I am trying to fit data points based on cone fitting. I have developed a code but there is an error that is always coming up:

Pixel_coordinates_of_the_inside_vortex

Error using lsqcurvefit

Function value and YDATA sizes are not equal.

Error in Pixel_coordinates_of_the_inside_vortex (line 20)

paramsFit = lsqcurvefit(@(params, xy) coneEquation(params, xy), initialGuess, xyData, z);

My code is:

theta = linspace(0, 2*pi, 100);
r = linspace(0, 5, 100);
z = linspace(0, 10, 100);
xData = r .* cos(theta);
yData = r .* sin(theta);
% Define the cone equation as a function
coneEquation = @(params, xy) sqrt(xy(:,1).^2 + xy(:,2).^2) * tan(params(1)) - params(2);
% Initial guess for parameters (angle and height)
initialGuess = [pi/4, 5];
% Concatenate xData and yData into a single matrix
xyData = [xData(:), yData(:)];
% Fit the cone equation to the data using lsqcurvefit
paramsFit = lsqcurvefit(@(params, xy) coneEquation(params, xy), initialGuess, xyData, z);
% Extract the fitted parameters
angle = paramsFit(1);
height = paramsFit(2);
% Display the equation of the fitted cone
fprintf('Fitted Cone Equation: sqrt(x^2 + y^2) * tan(%.4f) = %.4f\n', angle, height);
% Create a grid of points for the fitted cone plot
[X, Y] = meshgrid(linspace(min(xData), max(xData), 100), linspace(min(yData), max(yData), 100));
XY = [X(:), Y(:)]; % Concatenate X and Y into a single matrix
Z = sqrt(X.^2 + Y.^2) * tan(angle);
% Plot the data points and the fitted cone surface
figure;
scatter3(xData, yData, z, 'o', 'filled');
hold on;
surf(X, Y, Z, 'FaceAlpha', 0.5);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Cone Curve Fitting');
hold off;

Answer 1

[Matt J]

Consider using rightcircularconeFit(), which is non-iterative, from this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

Answer 2

[Walter Roberson]

theta = linspace(0, 2*pi, 100);
r = linspace(0, 5, 100);
z = linspace(0, 10, 100);
xData = r .* cos(theta);
yData = r .* sin(theta);
% Define the cone equation as a function
coneEquation = @(params, xy) sqrt(xy(:,1).^2 + xy(:,2).^2) * tan(params(1)) - params(2);
% Initial guess for parameters (angle and height)
initialGuess = [pi/4, 5];
% Concatenate xData and yData into a single matrix
xyData = [xData(:), yData(:)];
% Fit the cone equation to the data using lsqcurvefit
paramsFit = lsqcurvefit(@(params, xy) coneEquation(params, xy), initialGuess, xyData, z(:));

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

% Extract the fitted parameters
angle = paramsFit(1);
height = paramsFit(2);
% Display the equation of the fitted cone
fprintf('Fitted Cone Equation: sqrt(x^2 + y^2) * tan(%.4f) = %.4f\n', angle, height);

Fitted Cone Equation: sqrt(x^2 + y^2) * tan(1.1071) = -0.0000

% Create a grid of points for the fitted cone plot
[X, Y] = meshgrid(linspace(min(xData), max(xData), 100), linspace(min(yData), max(yData), 100));
XY = [X(:), Y(:)]; % Concatenate X and Y into a single matrix
Z = sqrt(X.^2 + Y.^2) * tan(angle);
% Plot the data points and the fitted cone surface
figure;
scatter3(xData, yData, z, 'o', 'filled');
hold on;
surf(X, Y, Z, 'FaceAlpha', 0.5);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Cone Curve Fitting');
hold off;