How to find the arclength and radius of curvature for a set of 3D data points?

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Matthew Wong
Matthew Wong 2018-11-5
评论： Matthew Wong 2018-11-16
I have a set of 3-D points that represent the coordinates of a curve. I need to find the arclength and radius of curvature of this curve. How might I go about doing this? I've tried fitting the data to a polynomial but it doesn't seem to be working. Please Help!
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Matthew Wong
Matthew Wong 2018-11-12
Thanks for the feedback guys! I've attached my data this time. Basically right now I try to break up the data into smaller sections that encompass only one section of the curve so that it better fits a polynomial. Then I use the 'fit' equation to go through and try to fit a polynomial to each section. Then I try to find the arclength of each section (Right now I'm only trying to calculate the arclength, after I get a correct fit for the data I'll move on to radius of curvature).
if true
%Initialize empty arrays and variables to prevent memory overload
syms s x y;
Pts = zeros(100,3);
magnitudes = zeros(99,1);
dx = zeros(99,1);
dy = zeros(99,1);
dz = zeros(99,1);
dscore = zeros(99,1);
magdiff = zeros(99,1);
Sigpts = zeros(100,3);
lowbound = 1;
fitdata=zeros(100,3);
arclength=zeros(100,1);
%Load points into a 100 x 3 array
for j=1:100
Pts(j,1) = xpts(j);
Pts(j,2) = ypts(j);
Pts(j,3) = zpts(j);
end
%Plot the curvature
%plot3(Pts(:,1),Pts(:,2),Pts(:,3));
% grid on;
hold off;
end
Matthew Wong
Matthew Wong 2018-11-12
Update: I had some trouble posting my entire code, but I've attached the MATLAB file above.

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Are Mjaavatten
Are Mjaavatten 2018-11-16
编辑：Are Mjaavatten 2018-11-16
I was inspired by your question to write a functon that calculates the arc length and curvature of a 1D curve in 2D or 3D space. I believe that does what you want. I submitted it to The Mathworks File Exchange today. You will find it here.

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