How to plot the best fitted ellipse or circle?

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Ashfaq Ahmed
Ashfaq Ahmed 2023-10-24
编辑： Matt J 2023-10-25
Ran in:
Hi all,
I have a data set (attached here) that has two arrays. I want to plot them in a polar graph and want to find out the best fitted a) ellipse, and b) circle.
x(:,1) is the x and x(:,2) is the y for the plot.
If anyone can help me out here, I will be very grateful.
xy = load("EllipseData.mat");
x = xy.x(:,1);
y = xy.x(:,2);
plot(x,y,'o')
axis equal
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Ashfaq Ahmed
Ashfaq Ahmed 2023-10-25
编辑：Ashfaq Ahmed 2023-10-25
Hi @Image Analyst, the secoond option. It would be if they are plotted in the polarplot first and then creating the ellipsoid.
Image Analyst
Image Analyst 2023-10-25
I see you accepted @Matt J's answer. You can adjust/control the approximate number of points within the ellipse by changing the 0.95 in this line of code:
b=boundary(XY,0.95);

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Matt J
Matt J 2023-10-25
编辑：Matt J 2023-10-25
Ran in:
The code below uses ellipsoidalFit() from this FEX download,
https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics
Is this the kind of thing you are looking for?
xy=load('EllipseData.mat').x;
p=prunecloud(xy);
Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.
I=all(~isnan(p.Vertices),2);
e=ellipticalFit(p.Vertices(I,:)');
%Display -- EDITED
XY=e.sample(linspace(0,360,1000));
[t,r]=cart2pol(xy(:,1),xy(:,2));
[T,R]=cart2pol(XY{:});
polarplot(t,r,'ob',T,R,'r-')
function [p,XY]=prunecloud(xy)
for i=1:3
D2=max(pdist2(xy,xy,'euclidean','Smallest', 10),[],1);
xy(D2>0.1,:)=[];
end
XY=xy;
b=boundary(XY,0.95);
p=polyshape(XY(b,:));
end
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Ashfaq Ahmed
Ashfaq Ahmed 2023-10-25
Hi @Matt J, thank you for the suggestion. I can see it is working now. I have a request. Can you please help me plot it on a polar plane?

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更多回答（3 个）

Image Analyst
Image Analyst 2023-10-24
Torsten
Torsten 2023-10-24
编辑：Torsten 2023-10-24
  1. Compute the center of gravity of the point cloud. Call it (x',y').
  2. Compute the point of your point cloud with the greatest distance to (x',y'). Call the distance R.
  3. Define the circle that encloses the point cloud by (x-x')^2 + (y-y')^2 = R^2.
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Les Beckham
Les Beckham 2023-10-25
移动：Image Analyst 2023-10-25
Ran in:
xy = load("EllipseData.mat");
x = xy.x(:,1);
y = xy.x(:,2);
rho = sqrt(x.^2 + y.^2);
theta = atan2(y,x); % <<< use 4 quadrant atan2
polarplot(theta, rho, '.', 'markersize', 3, 'Color', '#aa4488')

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