1. In one sentence, explain what the following homogeneous transformation accomplishes when applied to a point...

 

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1. In one sentence, explain what the following homogeneous transformation accomplishes when applied to a point (x, y, z), in terms of yaw, pitch, roll, and translation. T₁ = 0 0 0 0 2 1 0 0 - I Z 1 2. Write out the 4x4 homogeneous transformation T2, when applied to a point (x, y,z) in global coordinate frame, translates the point by (3,0,2), then followed by a pitch of 45 degrees. Your answer need not be simplified, and may be represented as a single matrix or the product of two or more matrices. 3. We would like to reverse the transformation applied by T₂T₁, that is, write out (T₂T₁)¹. Your answer need not be simplified, and may be represented as a single matrix or the product of two or more matrices. 4. Write out the Quaternion equivalent to the rotations in T₁ and T₂as 9₁ and 92- Then calculate the product, that is, 9₁ 92 (Hint: Steve's book may be a good source of reference) 1. In one sentence, explain what the following homogeneous transformation accomplishes when applied to a point (x, y, z), in terms of yaw, pitch, roll, and translation. T₁ = 0 0 0 0 2 1 0 0 - I Z 1 2. Write out the 4x4 homogeneous transformation T2, when applied to a point (x, y,z) in global coordinate frame, translates the point by (3,0,2), then followed by a pitch of 45 degrees. Your answer need not be simplified, and may be represented as a single matrix or the product of two or more matrices. 3. We would like to reverse the transformation applied by T₂T₁, that is, write out (T₂T₁)¹. Your answer need not be simplified, and may be represented as a single matrix or the product of two or more matrices. 4. Write out the Quaternion equivalent to the rotations in T₁ and T₂as 9₁ and 92- Then calculate the product, that is, 9₁ 92 (Hint: Steve's book may be a good source of reference)

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