Calculate the angle between multiple points

I have a matrix A contain x values in the first column and y values in the second column. I want to calculate the angle between vectors.

[Jan]

There is no "angle between points". Do you mean the angle between two vectors?

Answer 1

[Jan]

The ACOS and the corresponding ASIN approchs are numerically instable near to multiples of pi (half). Better use the more accurate ATAN2 method:

angle = atan2(norm(cross(v1,v2)), dot(v1,v2));

[Roger Stafford]

In the two-dimensional x-y plane Mathworks' 'cross' function doesn't work. It requires three-element vectors. The two-dimensional expression should be:

 angle = atan2(abs(det([v1;v2])),dot(v1,v2));

where v1 and v2 are assumed to be two-element row vectors.

(Corrected)

[Jan]

@Roger: Thanks! I forgot the limitations of cross.

[Stephen Devlin]

Hi, I have no idea if anyone will see this comment as it is years after the original post, but mathematically what is this expression:

"angle = atan2(abs(det([v1;v2])),dot(v1,v2));"

[Jess Smith]

@stephen thats basically doing the inverse tangent of the cross product of 2D vectors over the dot product of those vectors, giving you the angle; cross product of a x b is |a||b|sin(theta) and dot product is |a||b|cos(theta) so dividing them by each other and taking inverse tan is the angle

Answer 2

[michael scheinfeild]

what is v1 v2 can yo give example