3D system definition: How btaining the angle between a single axis and a plane

Hello, I am having trouble obtaining the angle between a vector and a plane which are defined by two different rotation matrix.

I have two objects, A and B, which are defined by rotation matrices R (Rotation matrix from global origin to A) and R' (Rotation matrix from global origin to B).

R = [a b c; d e f; g h i]

R'= [a' b' c'; d' e' f'; g' h' i']

I want to obtain the rotation in degrees between the axis X from object A to the plane XZ (and eventually XY) from object B.

Thank you in advance.

Alonso

Answer 1

[Matt J]

and eventually XY

That would just be the angle between Yprime and Z, wouldn't it?

Yprime=Rprime(:,2);
Z=R(:,3);

angle = acosd( dot(Yprime,Z)/norm(Yprime)/norm(Z) )

[Luis FigueroaFernandez]

I dont think I explained correctly.

It would be the angle between axis X and plane X'Z' and between X and plane X'Y'.

My apologies

[Matt J]

Same sort of thing...

X=R(:,1);
Yprime=Rprime(:,2);
Zprime=Rprime(:,3);

angle1 = 90-acosd( dot(Yprime,X)/norm(Yprime)/norm(X) ) %Angle with plane X'Z'
angle2 = 90-acosd( dot(Zprime,X)/norm(Zprime)/norm(X) ) %Angle with plane X'Y'

[Luis FigueroaFernandez]

Thank you!