(5 pts) Given a 2-D starting point at position (25, 50), provide the matrix needed for a translation of (10, 20) and the point resulting from that translation. Next provide the matrix for a rotation of 90 degrees and the result of rotating the previous translated point. Finally provide the matrix for scale factors of (1.5, 2.0) and the result of scaling the previously rotated point.. You should use 3 x 3 matrix math for this problem.
(5 pts) Refer back to problem 1. Compute the product of three matrices you provided. Be sure to compute the product in the correct order to reflect the transformations in the same order as in that problem. Apply the product matrix to the same original starting point and compute the resulting point.
Product of three transformations can be written as
(5 pts) Given a line segment with endpoints (2. 5) and (9, 15), provide the equation for that line segment using a parameterized representation. Determine whether the point with a x ordinate of 8 and the point with a y ordinate of 20 are within that line segment. Show how you made the determination. Explain the role of such calculations in clipping algorithms.
(5 pts) Given a 3-D point at position (0, 1, 0). Provide the matrix for a 90 degree rotation around the x-axis. Determine the point that results from performing that rotation on the original point. Next provide the matrix for a 45 degree rotation around the y-axis. Determine the result from performing the y-rotation on the point that resulted from the previous rotation. Finally provide the matrix for a 180 degree rotation around the z-axis. Determine the result from performing the z-rotation on the point that resulted from the previous rotation. Because no translations are involved, you can use 3 x 3 matrix math for your calculations.
(5 pts) Using quaternions, perform the same three rotations on the same original point in problem 4. Show the quaternion and its conjugate used for each rotation and the quaternion that results after using that quaternion to perform the rotation.
