Methods to calculate curvature

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L_Del
L_Del 2019-6-25
回答： L_Del 2019-6-25
Hi all,
I am trying to calculate the curvature of a series of points. The distance in x between those points is never the same. The distance (in x,y) also varies between 0 and 1.
I tried both these functions (https://www.mathworks.com/matlabcentral/fileexchange/69452-curvature-of-a-2d-or-3d-curve and https://www.mathworks.com/matlabcentral/fileexchange/32696-2d-line-curvature-and-normals) without success.
The problem: Sometimes, when the distance (in x,y) is really small (0.1) , the curvature (respectively the radius) of a straight line becomes too big (respectively small) when it should be the opposite. I think the distance in x,y or perhaps just in x should stay the same for it to work. But I can't be really sure. Does the distance play that big a role? Could it be linked to noise in the series of points? If so, what should I do to get accurate results?
Thank you in advance for your help.
Regards,
LD
  2 个评论
Jan
Jan 2019-6-25
Please explain this sentence: "the curvature (respectively the radius) of a straight line becomes too big (respectively small) when it should be the opposite" The curvature of a straight line should be 0, so I do not understand "too big" and "respectively small". 0.1 does not sound "really small".
Of course noise influence the results. For a line, which is expected to be straight, a curvature different from 0 is even dominated by noise. So please post more details, preferrably some data, which demonstrate the observed effect.
L_Del
L_Del 2019-6-25
Thank you for your post. I got things mixed up. Sorry about that.
Here is the output data which shows the issues I'm experiencing. I have to host it on dropbox for confidentiality reasons. It'll have to be removed once we figure this out.
The two first fields are the x and y coordinates, the third one is the distance in x,y , the fourth one is the calculated radius between the previous and the next points using this function. The last field is the speed obtained with v=sqrt(Acceleration*Radius).
NB: - You can plot x and y to visualise the path.
- I have to fix a few bugs for example at row 220,221 etc... but this isn't related to my issue.
- The distance between two following points decreases. I used Bezier curves to model my path . Here is the code I used. Each time a new Bezier curve is used, the distance suddenly gets bigger before decreasing slowly.
For example, the point at row #245 has an associated speed of 47m/s, which is small because the radius is small. The radius shouldn't be small at this point as it's on a straight line.

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回答（1 个）

L_Del
L_Del 2019-6-25
I think the problem might come from the fact that the x values are not evenly spaced out. I did a test with a simple sine curve and was able to get proper radii. For this test, the distance in x was the same for every point as I used linspace to define the x values...
If so, how can I create a new matrix from the existing data with x values evenly spaced out? I tried interp1 without success...

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