how to calculate degree between 3 points in MATLAB?

hi, how can i caculate degree between 3 points? i have position of X and Y of this three points. for more information please see this picture ( http://theme.tk/wp-content/uploads/2013/01/Untitled1.png ) and download this file ( http://theme.tk/wp-content/uploads/2013/01/data.zip ).

[Azzi Abdelmalek]

In your image there are 4 points? Can you be more clear by giving an example of coordinates

[Mahan Soltani]

yes,but i need degree that is red and (?degree). degree between two line(L-Knee point & Calcaneus) and (Calcaneus & 2th_MT). this image is a motion analys that i need degree of Ankle. some of data is : ( http://theme.tk/wp-content/uploads/2013/01/data-1.zip ) .

Answer 1

[Roger Stafford]

Let row vectors P0 = [x0,y0], P1 = [x1,y1], and P2 = [x2,y2] be Calcaneus, L-Knee, and 2th_MT points, respectively. The angle shown in red in radians at Calcaneus point is:

 ang = atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0));

Multiply by 180/pi to get degrees.

Roger Stafford

[Image Analyst]

I'm sure he's going to ask if that also works in 3D.

P0 = [x0, y0, z0];
P1 = [x1, y1, z1];
P2 = [x2, y2, z2];
theAngle = atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0));

[Roger Stafford]

No, that doesn't work. In three dimensions it would have to be:

 ang = atan2(norm(cross(P2-P0,P1-P0)),dot(P2-P0,P1-P0));

(This for three dimensions.)

[Image Analyst]

Thanks. I gave you a vote and mohammad should mark this as the answer. To get the answer in degrees, you can use atan2d() instead of atan2().

[Mahan Soltani]

hi Roger,thanks 4 your attention , i have this note file ( http://theme.tk/wp-content/uploads/2013/01/Position-Ankle.zip ) . can you write a command that calculate Ankle degree in each time??? i need a MATLAB code that finaly shows this Angels: ( http://theme.tk/wp-content/uploads/2013/01/Final-Angel.zip ) .

[Image Analyst]

If you did it, it would be done by now. Why do you think Roger should do it for you? Why can't/won't you do it?

[Mahan Soltani]

this error occured Image Analyst : Undefined function 'atan2d' for input arguments of type 'double'.

[Roger Stafford]

I believe what you are asking for is a vectorized version of the above formula. The 'cross', and 'dot' functions both work in vectorized form but 'norm' doesn't, so it has to be written as follows.

Let P0, P1, P2 be three two-dimensional n by 3 matrices with each row of three elements the coordinates of the points and successive rows corresponding to successive positions in time. To get the angle in degrees do:

 ang = atan2(sqrt(sum(cross(P2-P0,P1-P0,2).^2,2)),dot(P2-P0,P1-P0,2))*180/pi;

[Mahan Soltani]

thanks a lot Roger, your code is true , and if you see the text file, i have very number and points. give me a code that import those text file to matlab and calculate Angel for any time ( row ). merc

[Roger Stafford]

No mohammad, I think you had better do that. That last vectorized formula I presented will have to suffice for my contribution to your effort.

[Mahan Soltani]

Learning MATLAB on this time is hard and confusing for me. my field is Physical Therapy and i can't uderstand MATLAB very well...

Answer 2

[Image Analyst]

Check out this link:

http://www.mathworks.com/matlabcentral/answers/11580#answer_15786

[Mahan Soltani]

on those post, 2 point are available, but i need 3 point which one of them isn't (0 0 0)! if you see image, you could uderstand...

[Image Analyst]

Try this one then: http://www.mathworks.com/matlabcentral/newsreader/view_thread/276582 or do your own search.