MATLAB: Measure angles between two vectors solely counter – clockwise

MATLABvector manipulationvectors

Hi,

I have two vectors and I want to measure the angle between them. The first one lies solely along the positive x-axis, and the second one varies in a circle. When the angle between the two gets greater than 180 degrees, MATLAB starts to measure the angle clockwise, but I would like it to continue to measure the angle counter clockwise. (e.g, after 180, measure 190, 200 etc.. instead of 170, 160 etc..). Any workarounds? Stuff like atan2 doesn't work. Thanks in advance!

Best Answer

Hi Harvey,

It looks like you want the angle in degrees. For two dimensions, where the second vector has components x,y:

theta = mod(atan2d(y,x)+360,360)

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MATLAB: Increase compute speed compute angle between 2 vectors

The indirection of anonymous functions costs time. So either use the built-in functions with the same names cross, norm and dot, or hard code the functions directly.

Instead of the expensive trick to determine the positions of instabilities in the ASIN and ACOS methods, use a stable method directly:

atan2(norm(cross(N1 x N2)), dot(N1, N2))

Where N1 and N2 are the normalized input vectors.

N1      = bsxfun(@rdivide, a, sqrt(sum(a .* a ,1)))
N2      = bsxfun(@rdivide, b, sqrt(sum(b .* b ,1)))
N1dotN2 = N1(:, 1) .* N2(:, 1) + N1(:, 2) .* N2(:, 2) + N1(:, 3) .* N2(:, 3);
N1xN2   = [(N1(:, 2) .* N2(:, 3) - N1(:, 3) .* N2(:, 2)), ...
         (N1(:, 3) .* N2(:, 1) - N1(:, 1) .* N2(:, 3)), ...
         (N1(:, 1) .* N2(:, 2) - N1(:, 2) .* N2(:, 1))];
Angle   = atan2(sqrt(sum(N1xN2 .* N1xN2, 1)), N1dotN2);

MATLAB: Orthagonal planes and normal vectors

Hi M,

A plane satisfies the dot product equation equation

r dot v = const

where r is the position vector [x y z] and v = [vx vy vz] is a vector perpendicular to the plane. A vector perpendicular to the first plane is

v1 = [3 2 -1];

because dotting that into [x y z] produces the equation for the first plane. Similarly for the other two. A unit vector perpendicular to the plane is

n1 = v1/norm(v1)   % normalized vector perpendicular to plane

and similarly for the other two. Then dot(n1,n2) tellls you if n1 and n2 are orthogonal, and similarly for the other possible pairs.

Planes are orthogonal if and only if their normal vectors are orthogonal.

Best Answer

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MATLAB: Increase compute speed compute angle between 2 vectors

MATLAB: Orthagonal planes and normal vectors

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