Given a point P (2, 4, 8) and using the homogeneous representation: a. Calculate the corresponding...

 

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Given a point P (2, 4, 8) and using the homogeneous representation: a. Calculate the corresponding transformation matrix and the coordinates of the transformed point P* if P is rotated about the x, y, and z axes at angles of 30, 60, and 90°, respectively. b. If the point P obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. Verify your answer. c. Calculate P" if P is translated by d = 31 – 4j – 5k and then scaled uniformly by S = 1.5. d. Calculate the orthographic projection of P, of P. e. Calculate the perspective projection P, of P if the center of projection is at distance d = 10 from the origin along z-axis. Y, Y, Note The generalization for Perspective Projection presented in the lecture can be presented in the Liigh following homogenous form: [1 0 0 1 0 0 [o 0 -1/d 1. 01 0|ly 0||z X.X, P, = Given a point P (2, 4, 8) and using the homogeneous representation: a. Calculate the corresponding transformation matrix and the coordinates of the transformed point P* if P is rotated about the x, y, and z axes at angles of 30, 60, and 90°, respectively. b. If the point P obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. Verify your answer. c. Calculate P" if P is translated by d = 31 – 4j – 5k and then scaled uniformly by S = 1.5. d. Calculate the orthographic projection of P, of P. e. Calculate the perspective projection P, of P if the center of projection is at distance d = 10 from the origin along z-axis. Y, Y, Note The generalization for Perspective Projection presented in the lecture can be presented in the Liigh following homogenous form: [1 0 0 1 0 0 [o 0 -1/d 1. 01 0|ly 0||z X.X, P, =

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