How to fit the data points into a closed curve?
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Hello everyone, I’d like to ask you a question. Now I have a series of data points and want to fit these points into a closed curve. But the effect is not good, I would be very grateful if anyone can help me. The data required for closed curve fitting is shown below.
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John D'Errico
2020년 11월 26일
Please don't use an answer just to make a comment. I've moved your answer into this comment.
John D'Errico
2020년 11월 26일
What about that data do you want to be a closed curve? No, you cannot use interpolation using tools like interp1 to fit the black curve.
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Stephan
2020년 11월 26일
This will not solve your problem finally, but it shows a possible way to tackle this. The idea here is to use a cardiod curve and find parameters that try to minimize the difference between the single data points:
data = readmatrix('DataFit.xlsx');
a = [72.0839, 1.3643, 338.485, 289.4648, -21];
[x,y] = calcCurve(a);
figure
scatter(data(:,1),data(:,2))
hold on
scatter(x,y)
hold off
function [x,y] = calcCurve(a)
theta = linspace(-pi,pi,1187);
r = @(theta) a(1).*(a(2)+cos(theta));
rho = r(theta);
[x,y] = pol2cart(theta,rho);
x = -x';
y = -y';
xy = sortrows([x,y],1);
x = xy(:,1) + a(3);
y = xy(:,2) + a(4);
end
The parameters for a were found by optimization techniques - maybe this is a local optimum and we could do better. But the point is, that you have to think about your mathematical problem and analyze what you have there. After that it makes sense to start coding:
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