CSE3541/5541 (Summer 2022) Homework #1

I.      Preparation

Study the course lecture notes before attempting this assignment. All questions can be answered from course material.

II.      Collaboration & Piazza

Please read the course policy on Academic Misconduct in the syllabus. You may discuss the problems with your classmates at a high level only. Though, you must formulate your own solution without any help from others or third party sources.

In your solution, you need to list with whom you have discussed for each problem (please do so in the first page).

Do not post any part of your solution or spoilers on Piazza.

III.      Guidelines

You will place your solution into a single PDF file named HW3_name_dotnumber.pdf (e.g., HW3_shareef_ 1.pdf).

It is highly suggested that you directly type your solutions and save them as a PDF file. If you write your solutions on paper and scan it you run the risk that the TA won’t be able   to read your solution. In this case the TA will not give credit for any portion that is not     readable.

IV.      Problems

NOTE: For each problem, please show all work and then clearly state your final    answer. Just writing a final answer (even if correct) with little to no work will         receive little to no credit. Credit will be based upon your work to arrive at the final answer.

0)  List with whom you have discussed the homework in any way. If you did not discuss  with anyone then write “No discussions” . Remember that all discussions must only be at a high level. Do not share your work or look at other student’s work. Do not use      third party sources.

1)  (10 points) A framebuffer using the rgb color channels has a screen resolution with an equal number of pixels in each dimension (i.e., width and height) for a total of   1,048,576 pixels. Each color channel is represented with 1 byte each. How much    video memory will the framebuffer need in bytes? Show all work.

1                      3

1                      1

expressed in homogeneous coordinates). You want to uniformly scale point 2 by   1/2 and then rotate point 2 by 45 degrees. Though, you want to perform these two operations about point 1 , i.e., not the origin. After this transformation, the new

location of the point 2  is ′2  = |1 + √2 |.

a.   (10 points) You will need four 3 × 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each.       Entries in all matrices must have numeric values.

b.   (10 points) Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the        transformation.

c.   (10 points) Add the point 2 to the matrix sequence in part (b) and       complete the multiplication. Show the result of each multiplication you perform. Your final answer should be point ′2 .

3)  Consider vectors  = (−4, 5, 6) and  = (3, 2, 1).

a.   (10 points) Compute the angle, in degrees, between vectors  and  .      Write your initial equation (without values) and then show all steps to compute the angle.

b.   (10 points) Compute the length of the projection of vector  onto  .      Write your initial equation (without values) and show all steps to        compute the projection. Show all intermediate equations that you use and their solutions. For example, if you need to compute the length of