Problem 1 - Rotation (40 pts) In this problem, you will experiment with two different ways of performing rotation Problem 1.1 (10pts) Implement a Matlab function for rotating a 3D point around an axis of rotation ProtrotateAzis(v, 0, p) Here v is a 3 x 1 vector for the axis of rotation, 0 is the angle of rotation in radian. P, Prot are both 3 x 1 column vectors. Prot is obtained by rotating p an angle 0 around the axis v. In this question, suppose you do not know about quaternion. You cannot use quaternion for this question Problem 1.2 (15pts) Implement a Matlab function for rotating a 3D point using quaternion. Prot rotateQuat(q, p) Here q is 4 x 1 vector representing an unit quaternion (q (w, [v, v2, v31), d p, prot are both 3 x i column vectors. Prot is obtained by rotating p using quaternion q. Problem 1.3 (15pts) Derive the rotation matrix R for the rotation that is represented by an unit quaternion q - (w, [vi, v2, v3]). for this rotation. The elements of rotation matrix should be expressed in terms of w, vi, v2, vs. Show your derivation on paper. Problem 1 - Rotation (40 pts) In this problem, you will experiment with two different ways of performing rotation Problem 1.1 (10pts) Implement a Matlab function for rotating a 3D point around an axis of rotation ProtrotateAzis(v, 0, p) Here v is a 3 x 1 vector for the axis of rotation, 0 is the angle of rotation in radian. P, Prot are both 3 x 1 column vectors. Prot is obtained by rotating p an angle 0 around the axis v. In this question, suppose you do not know about quaternion. You cannot use quaternion for this question Problem 1.2 (15pts) Implement a Matlab function for rotating a 3D point using quaternion. Prot rotateQuat(q, p) Here q is 4 x 1 vector representing an unit quaternion (q (w, [v, v2, v31), d p, prot are both 3 x i column vectors. Prot is obtained by rotating p using quaternion q. Problem 1.3 (15pts) Derive the rotation matrix R for the rotation that is represented by an unit quaternion q - (w, [vi, v2, v3]). for this rotation. The elements of rotation matrix should be expressed in terms of w, vi, v2, vs. Show your derivation on paper