How do you perform rotation about an arbitrary axis in 3D with diagram?

How do you perform rotation about an arbitrary axis in 3D with diagram?

Rotation about Arbitrary Axis

1. Translate the object to the origin.
2. Rotate object so that axis of object coincide with any of coordinate axis.
3. Perform rotation about co-ordinate axis with whom coinciding is done.
4. Apply inverse rotation to bring rotation back to the original position.

What are the steps of rotation about arbitrary axis?

Rotate a point about an arbitrary axis (3 dimensions)

1. (2) rotate space about the x axis so that the rotation axis lies in the xz plane.
2. (3) rotate space about the y axis so that the rotation axis lies along the z axis.
3. (4) perform the desired rotation by theta about the z axis.
4. (5) apply the inverse of step (3)

How to rotate an arbitrary axis in three dimensions?

(1) Translate space so that the rotation axis passes through the origin. (2) Rotate space about the z axis so that the rotation axis lies in the xz plane. (3) Rotate space about the y axis so that the rotation axis lies along the z axis. (4) Perform the desired rotation by θ about the z axis. (5) Apply the inverse of step (3).

How to calculate the axis of rotation of a line?

We will define an arbitrary line by a point the line goes through and a direction vector. If the axis of rotation is given by two points P1 = ( a,b,c) and P2 = ( d,e,f ), then a direction vector can be obtained by ⟨u,v,w⟩ = ⟨d−a,e−b,f −c⟩. We can now write a transformation for the rotation of a point about this line.

How to rotate space along the Y axis?

The rotation matrix Rx and the inverse Rx-1 (required for step 6) are given below Rotate space about the y axis so that the rotation axis lies along the positive z axis. Using the appropriate dot and cross product relationships as before the cosine of the angle is d, the sine of the angle is a.

How to rotate a 3D vector by angle theta?

To rotate a 3D vector “p” by angle theta about a (unit) axis “r” one forms the quaternion Q 1 = (0,p x,p y,p z) and the rotation quaternion Q 2 = (cos (theta/2), r x sin (theta/2), r y sin (theta/2), r z sin (theta/2)).