CPSC 453, Winter ’15, Midterm CPSC 453, Winter 2015, Midterm Exam (Take Home) Released: March 10th, 2015 DUE: March 19th, 2015 (Thursday) in class Full Name: ______________________________________________ Student ID: __________________________________________ This exam is individual work. 15% of the final grade Print it out, fill your name and ID, carefully answer all the questions and hand it in on March 19th, 2015 in class Please use BLUE pen to answer your questions Late hand-ins will NOT be accepted Question # Points Your Points Q1 8 Q2 8 Q3 4 Q4 5 Q5 4 Q6 2 Q7 10 Q8 7 Total 48 1 CPSC 453, Winter ’15, Midterm Q1: Circle out Vector (V) or Raster (R) displays? (8 pts) V R -- lines are smooth V R -- only lines possible, no filled polygons, or bitmaps V R -- discretized version of the model V R -- close to the 'pure mathematics' of the model V R -- no flicker V R -- jagged edges V R -- constant time to redraw any number of elements V R -- slower with more elements to be drawn, can start to flicker Q2: Four-Universe Paradigm – For each problem below, circle which ‘universe’ the corresponding component belongs to. (8 pts) Problem #1 – Virtual Camera (1 pt for each problem component) Problem Component Four Universes Projective transformations P M R I (…) gluLookAt(10.0,15.0,10.0,3.0,5.0,-2.0,0.0,1.0,0.0) (…) gluPerspective(40.0,1.5,50.0,100.0) (…) P M R I P M R I P M R I Photographic camera 2 CPSC 453, Winter ’15, Midterm Problem #2 – 2D Image Modeling (1 pt for each problem component) Problem Component Four Universes A = [ai, j], i = 1,...,m; j = 1,...,n P M R I Black & White photo P M R I P M R I P M R I Point sampling Q3: Transformations. (4 pts) Show that the translation represented by [T] affects points but not vectors. u1 x Consider the 2D case. Let P y be a point and u u 2 be a vector. 0 1 (a) Fill in the blanks (2 pts) _______ 1 0 tx x [T ]P 0 1 ty y _______ 0 0 1 1 _______ _______ 1 0 tx u1 [T ]u 0 1 ty u 2 _______ 0 0 1 0 _______ (b) Your justification analysis based on the results from the above two transformations (2 pts): (b.1) what happened to point P after it is transformed by matrix [T]? (1 pt) (b.2) what happened to vector u after it is transformed by matrix [T]? (1 pt) 3 CPSC 453, Winter ’15, Midterm Q4: Which of the following pairs of transforms can be reversed without affecting the result (that is, applied in reverse order)? Circle out Y if they can be reversed and N if they cannot. (5 pts) Y N -- Translate(1,2)* Translate (2,3) Y N -- Scale(2,1) * Rotate(45) Y N -- Rotate(45) * Translate(1,1) Y N -- Rotate (10) * Rotate (20) Y N -- Scale(2,2) * Rotate(45) Q5: Perform a 45 degrees rotation of triangle A(0,0), B(1,1), C(5,2) – IMPORTANT: you must show the actual numerical values for the transformation matrices and the new triangle coordinates. Fill in the blanks. (4 pts) sine 45 degrees = 0.707 and cosine 45 degrees = 0.707 (a) About the origin (1 pt for matrix R and 1 pt for the transformed triangle coordinates) _______ R _______ _______ _______ _______ _______ _______ _______ _______ _____ _____ _____ _____ _____ _____ A _____ B _____ C _____ (b) About P(-1,-1) (1 pt for matrix R and 1 pt for the transformed triangle coordinates) _______ R _______ _______ _______ _______ _______ _______ _______ _______ A _____ B _____ C _____ 4 CPSC 453, Winter ’15, Midterm Q6: Draw house A, and house B transformed by the appropriate commands in the given order: Identity() … drawHouseB(). The untransformed house is below. (1 pt each) Identity(); Scale(1, .5); Translate(-4, -2); drawHouseA(); Rotate(180); Translate(0, 2); drawHouseB(); Untransformed House House A House B 5 CPSC 453, Winter ’15, Midterm Q7: Use the number corresponding to a term or name below as an in the space provided answer if you think it is the best match for one of the concepts or terms on the next page. Each term may be used once, more than once, or not at all. (10 pts) 1. 2. 3. 4. 5. 6. 7. 8. 9. homogeneous point flicker world frame jaggies screen window GLUT reverse mapping Breseham 10. affine 11. topology 12. virtual camera 13. sampling ratio 14. graphics pipeline 15. Weiler-Atherton 16. linear 17. modeling transformations 18. clipping 19. refresh rate 20. projection 21. object frame 22. Cohen-Sutherland 23. true color 24. alpha 25. geometry Questions We often add this fourth ???? coordinate in 3-D graphics to provide a uniform matrix representation for the various transformations that are used. Answers A weighted sum of vectors is a ???? combination and is itself always a vector. Use the ???? to place objeects and cameras within the scene Once we have set up the scene (objects and virtual camera in place), we use ????.to create a 2D image A weighted sum of points must be ???? if the result is a point. The ???? clipping algorithm is the most general polygon clipping algorithm of those discussed in the textbook. The ???? is a useful analogy or metaphor that assists in understanding various viewing and perspective parameters. Build complex objects by placing individual parts within the main object and overall scene The discrete, grid-like structure of pixels gives rise to this visual artifact when straight lines are drawn on a raster display if the lines are not exactly vertical or horizontal. The entire process of creating and perceiving an image on a CRT or other display device starting with a software application program and ending with the human visual system and brain. 6 CPSC 453, Winter ’15, Midterm Q8: Circle either True or False about the Phong illumination Model. (7 pts) The shinier the surface the more light is specularly reflected True False Ambient component realistically models ambient lighting True False The rougher the surface the less light is diffusely reflected True False All of the terms used directly derive from physical laws True False Specular reflection is responsible for the highlights that are visible on shiny objects True False Diffuse component depends on the viewing direction True False If a blue object is illuminated by a white light source, the color of the diffuse reflection will be blue but that of the specular reflection will be white True False END OF EXAM 7

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