How do i detect/describe a curvature from a data-set of coordinates

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I have a data-set of coordinates that makes up a 2d body. It's a rectangular shape with one side curved or kinda circular. I would like to describe this curved side with a polyfit line so that I can be able to get the radius. How can I achieve this? Thank you for your very much!

Accepted Answer

Star Strider
Star Strider on 23 May 2019
The polyfit function will not give you the centre and radius of your arc.
This will:
t = linspace(-pi/4, pi/4, 10); % Create Data
r = 2.5; % Create Data
x = r*cos(t)+1; % Create Data
y = r*sin(t)+2; % Create Data
fcn = @(b) norm(((x(:)-b(1)).^2 + (y(:)-b(2)).^2) - b(3).^2); % Objective Function
B = fminsearch(fcn, rand(3,1)); % Estimate Parameters
Cx = B(1) % Center X-Coordinate
Cy = B(2) % Center Y-Coordinate
R = B(3) % Radius
% B = fsolve(fcn, rand(3,1))
figure
plot(x, y, 'pg')
hold on
plot(Cx, Cy, 'pb')
plot([Cx x(1)], [Cy y(1)], '-r')
hold off
grid
legend('Data', 'Centre', 'Radius')
axis equal
How do i detect-describe a curvature from a data-set of coordinates - 2019 05 23.png
Experiment with it to get the result you want.
  10 Comments
Conrade Muyambo
Conrade Muyambo on 24 May 2019
Edited: Conrade Muyambo on 24 May 2019
Thank you. That helped a lot. But is it now possible, with the start point of one arc and the end point of the second arc to fit a curve to describe the side?
Star Strider
Star Strider on 24 May 2019
As always, my pleasure.
No.
The arc parameters describe the arcs only.
I have no idea how to describe the sides, since that is not what you requested initially.
See my oiriginal Answer (the ‘Create Data’ assignments) to understand how to describe the arcs.

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More Answers (2)

Conrade Muyambo
Conrade Muyambo on 24 May 2019
It served the purpose sir! That was only a question. Thank you
  1 Comment
Star Strider
Star Strider on 24 May 2019
As always, my pleasure!
You can likely adapt my code to estimate the sides that are not part of the arcs, although since they are more linear that nonlinear, a linear or ‘slightly nonlinear’ regression could work.

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Conrade Muyambo
Conrade Muyambo on 24 May 2019
Edited: Conrade Muyambo on 24 May 2019
Okay I understand, i will work on it. I will post a different topic later, but not related to this regarding the same shape,.

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