Methods to calculate curvature

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

[Jan]

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]

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.

Answer 1

[L_Del]

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...