Question

Ompute the composite transformation that is the result of the following:

Rₓ(30)
Rᵧ(45)
R_z(-60)
a) Is this a rigid-body transformation? Explain.
b) Apply the composite transformation to what?

Answer 1

To compute the composite transformation, apply the individual rotations in the given order. Yes, it is a rigid-body transformation. Applicable to any object for position and orientation transformation.

Step-by-step explanation:

To compute the composite transformation, we need to apply the individual transformations in the given order. Let's start with the rotation around the x-axis, Rx(30). This rotation will rotate an object counterclockwise by 30 degrees around the x-axis.

Next, we apply the rotation around the y-axis, Ry(45). This rotation will rotate the object counterclockwise by 45 degrees around the y-axis.

Finally, we apply the rotation around the z-axis, Rz(-60). This rotation will rotate the object clockwise by 60 degrees around the z-axis.

Therefore, the composite transformation is Rx(30) Ry(45) Rz(-60).

(a) Yes, this is a rigid-body transformation because the object retains its shape and size after each rotation.

(b) The composite transformation can be applied to any object to transform its position and orientation based on the given rotations.