EECS 3431 - Fall 2020 Midterm Exam Name: N/A for online exams Student ID: N/A for onlune exams Important Instructions - Read all of them carefully! • You must sign, date and upload the Academic Honesty Declaration provided on the course’s website. Your exam will not be graded without a signed declaration. • To ensure fairness, you must stop writing the exam at 12:45pm or any time the invigilator requests so. • The exam must be your work. You are not allowed to communicate with anyone about the exam. • The exam is open book. • Each question is worth 5 marks, unless otherwise specified. • For multiple choice and true/false questions, 1/5th of the marks will be extracted for wrong answers. • All concepts and quantities are referred to as described in the context of this class. • Record your answers on a .csv file as described in eclass. Upload the file on eclass. If eclass goes down, email a copy to the instructor at
[email protected]. • Make sure you upload the correct file. Forgetting to do so, will not be a valid excuse. • Save your answers often, and upload copies to a backup online location in case your com- puter crashes. • Read all questions and start from the ones that seem easier to you. • In questions related to transformations the corresponding functions, such as translate, rot, scale, shear etc return matrices. That is, the product presented should be considered a matrix product. Note that “rot” and “rotate” both refer to rotation. 1 Questions Your Score Max Score 1-15 75 2 Question 1: [5] In which coordinate system do we normally define the parameters of the camera, such as eye location, reference point, up vector? (A) Viewing. (B) World. (C) Screen. (D) None of the above. Question 2: [5] In which coordinate system do we normally define the camera’s viewport param- eters top, bottom, left, right, near, far? (A) World. (B) Viewing. (C) Screen. (D) None of the above. Question 3: [5] What does the viewport transformation do? (A) Transforms object coordinates to viewing coordinates. (B) Transforms viewing coordinates to normalized device coordinates. (C) Transforms the normalized device coordinates to screen (device) coordinates. (D) None of the above. 3 Question 4: [5] Assume that the camera coordinate system V CS = (E, i, j,k) is given with re- spect to the world coordinate system WCS = (O,x,y, z). Assume that Mt = 1 0 0 Ex 0 1 0 Ey 0 0 1 Ez 0 0 0 1 , Mr = ix iy iz 0 jx jy jz 0 kx ky kz 0 0 0 0 1 The following matrix transforms points from the camera coordinate system (VCS) to the world coordinate system (WCS) , that is: Pwcs = MPvcs (A) M = MrMt. (B) M = M−1t M−1r . (C) M = MtMTr . (D) M = MtMr. (E) None of the above choices. Question 5: [5] The positions of an object’s vertices are normally streamed to a vertex shader in (A) World coordinates. (B) Viewing coordinates. (C) Screen ( Device) coordinates. (D) None of these choices. 4 Question 6: [5] Which of the following transformation does not preserves angles? (A) Uniform scale. (B) Rotation around an arbitrary axis. (C) A rotation followed by a translation. (D) All of these transformations. (E) None of these choices. Question 7: [5] Which series of 2D transformations produces the reflection of a two dimensional point about an arbitrary line y = ax+ b? Remember, the following are matrix products, i.e. P ′ = MP . (A) M = translate(0,-b) * rot(-arctan(a)) * scale(1,-1) * rot(arctan(a)) * translate(0,b) (B) M = translate(0,b) * rot(arctan(a)) * scale(-1,1) * rot(-arctan(a)) * translate(0,-b) (C) M = translate(0,b) * rot(arctan(a)) * scale(-1,1) * rot(arctan(a)) * translate(0,b) (D) M = translate(0,-b) * rot(-artctan(a)) * scale(-1,1) * rot(arctan( a)) * translate(0,b) (E) None of these choices. 5 PO x1 y1 A x2 y2 B x3 y3 Question 8: [5] What are the coordinates of point B in frame (O,x1,y1) ? (A) (1,3) (B) (-1,2) (C) (1,2) (D) (3,1) (E) None of these choices. Question 9: [5] What are the coordinates of point P in frame (A,x2,y2) ? (A) (0.5,1) (B) (0.5,0.5) (C) (0.5,2) (D) (1,1) (E) None of these choices. Question 10: [5] What are the coordinates of point A in frame (B,x3,y3) ? (A) (-0.5,0.5) (B) (1.5,-0.5) (C) (− √ 2, √ 2) (D) (1,2) (E) None of these choices. 6 Question 11: [5] Given a vector a 6= 0 and a triangle with unit normal vector n, what is the orthogonal projection of a on the triangle? n a (A) a · n. (B) a · n/ |a|. (C) a− (a · n)a. (D) a− (a · n)n. (E) None of these choices. Question 12: [5] Consider a 3D rotation around the x-axis by 30 degrees and a 3D translation by (3, 0, 0). The two transformations can be performed in any order. (A) False. (B) True. Question 13: [5] Assume that the camera parameters are: eye = (0, 10,−10), ref = (0, 10, 100), up = (0, 1, 0) in world coordinates. The camera is looking in the following direction in world co- ordinates: (A) (0, 1,−10). (B) (0, 0,−1) . (C) (0, 1, 0) . (D) None of these choices. Question 14: [5] Assume that the camera parameters are: eye = (1, 0,−5), ref = (1, 0, 100), up = (0, 1, 0) in world coordinates. The near plane is set at z = −12 in viewing (camera) coordi- nates. In world coordinates the near plane is: (A) z = 7 . (B) z = −10. (C) z = 100 . (D) z = −5. (E) None of these choices. 7 Question 15: [5] Assume two distinct 3D points, P1, P2 in homogeneous coordinates. Linearly combining these two points, e.g. P = aP1 + bP2, a, b ∈ < using their homogeneous repre- sentation produces: (A) A point. (B) A vector. (C) It depends. (D) None of these choices. 8
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