How To Find the Euler Angles(Roll,Pitch,Yaw) of a Plane in 3D?

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I am not sure if there is a way to find it. But I just wanted to ask it. Is there a way to find the Euler Angles (Roll, Pitch, Yaw) of a plane in 3D? Imagine that we have 3 points coordinates (P1(P1x,P1y,P1z), P2(P2x,P2y,P2z), P3(P3x,P3y,P3z)) in 3D space. By those points, we can find the plane equation which cooncide with P1,P2 and P3 points. We can assume that the plane equation is equal to A*x+B*y+C*z+D=0 .
From this plane equation, can we find the Roll, Pitch, Yaw angles of the corresponding plane?
R(r,p,y)=Rz(y)Ry(p)Rx(r) order or any other order which is described.

Answers (1)

Athul Prakash
Athul Prakash on 19 Jan 2021
Hi Ercan,
You mentioned that you have a plane equation of the form and wish to calculate the Euler angles. I presume you are referring to the angles that the plane's normal vector makes with the three axes. Further, these angles are the same as the angles with three axes-planes (eg: angle of normal with x-axis = angle of this plane with y-z plane)
The plane equation can be thought of as (where is a normal vthctor to the plane and is a variable point).
So the coefficients from the plane equation are the components of a normal vector ().
Thus, gives the angle 'α' with the x-axis. Similarly, you may calculate cosines of angles with the y and z axes as well. Obtaining the angles in radians is straightforward with the inverse cosine function.
Hope it helps!
ercan duzgun
ercan duzgun on 19 Jan 2021
Edited: ercan duzgun on 19 Jan 2021
Dear @Athul Prakash , I thought roll, pitch,yaw angles are different than what you expressed in your previous answer. Because; what you described is the angle between the plane and the x axis. However, what I need is the rotation angle around the x axis. I think they are different from each other. But I am not sure, because I got confused. Do you think I should try with another technique, but not by plane equation? And do you think that; your previous suggestion would be what I need for the Stewart Platform roll, pitch, yaw angles?
Thanks in advance.

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