Math  /  Geometry

QuestionActivity \#2 ( 15 min)\mathbf{1 5} \mathbf{~ m i n}) : Complete the following questions on the independent study topic of Computer Graphics. "NOTE: You are responsible for this topic and will be tested on it!* ( 10.8 \#4 in our text): View 13 is View 1 subject to the following five transformations:
1. Scale by a factor of 1/21 / 2 in the xx-direction, 2 in the yy-direction, and 1/21 / 2 in the zz direction.
2. Translate 1/21 / 2 unit in the xx-direction.
3. Rotate 2020^{\circ} about the xx-axis.
4. Rotate 45-45^{\circ} about the yy-axis.
5. Rotate 9090^{\circ} about the zz-axis. i) Construct the five matrices M1,M2,M3,M4,M5M_{1}, M_{2}, M_{3}, M_{4}, M_{5} associated with these 5 transformations. ii) If PP is the coordinate matrix of View 1 and PP is the coordinate matrix of View 13, express PP in terms of M1,M2,M3,M4,M5M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, and PP. You do NOT have to actually multiple these out...just set it up! \qquad

Vew 1
4 Vow 13
Activity \#3 ( -20 min ): Your TA will give you one or more eigenvalue/eigenvector questions to try. a) Complete the question by hand. b) Check your answer in MATLAB

Studdy Solution
Express the coordinate matrix P P' of View 13 in terms of M1,M2,M3,M4,M5 M_1, M_2, M_3, M_4, M_5 , and P P :
P=M5×M4×M3×M2×M1×PP' = M_5 \times M_4 \times M_3 \times M_2 \times M_1 \times P

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