finding the angle between a line and oblique axis

is there any way to find the angle between a line (vector) and its coressponding axis. I don't want to rotate to x-axis and work from there.

please refer to the attached image.

Answer 1

[Dev]

Hi @Suzuki,

We can compute the angle between a vector and an axis (X, Y or Z) directly without rotating any of the axes, using the dot product formula.

Given a vector v = [vx, vy] or [vx, vy, vz], and an axis unit vector:

• X-axis: u = [1, 0] or [1, 0, 0]
• Y-axis: u = [0, 1] or [0, 1, 0]
• Z-axis: u = [0, 0, 1] (for 3D)

The angle between vector ‘v’ and axis ‘u’ can be calculate as follows-

Θ = cos−1(v*u/∥v∥*∥u∥ ​)

We can compute the same using the “dot” and “acos” functions available in MATLAB. I have attached a reference code snippet below which achieves the same.

% Compute angle
cosTheta = dot(v, u) / (norm(v) * norm(u));
angleRad = acos(cosTheta);
angleDeg = rad2deg(angleRad);  % since acos returns angle in Radians

For more information regarding these functions, please refer to the documentation links using the below commands in your MATLAB terminal-

>> doc dot
>> doc acos

I hope the above explanation helps.