EXAMINATIONS 2017 TRIMESTER 2

Transcription

1 EXAMINATIONS 2017 TRIMESTER 2 CGRA 151 INTRODUCTION TO COMPUTER GRAPHICS Time Allowed: TWO HOURS CLOSED BOOK Permitted materials: Silent non-programmable calculators or silent programmable calculators with their memories cleared are permitted in this examination. Printed foreign language English dictionaries are permitted. No other material is permitted. Instructions: Attempt ALL questions. The examination will be marked out of 120 marks. Brief Processing documentation is provided on page??, which may be detached from the question paper. Answer in the appropriate boxes if possible if you write your answer elsewhere, make it clear where your answer can be found. There are spare pages for your working and your answers in this question paper. However, you may ask for additional paper if you need it. Questions: Marks 1. Programming in Processing Graphics algorithms Colour, displays, and human vision Mathematics for graphics 30 Total 120 CGRA 151 Page 1 of??

2 SPARE PAGE FOR EXTRA ANSWERS Cross out rough working that you do not want marked. Specify the question number for work that you do want marked. CGRA 151 Page 2 of??

3 Question 1. Programming in Processing [30 marks] (a) [15 marks] Write Processing code to draw the following things in the Processing window. The coordinates for drawing these things need to be specified to the nearest 10. Hint: the three circles have diameters 50, 80, and 120. ( Processing window) // Window size needs to be (300, 300) // CGRA 151 Page 3 of??

4 (b) [15 marks] Sketch what the following code will draw in the Processing window. size(300, 300); background(255); stroke(0); int x = 60; int y = 120; int i = 0; triangle(150,40,20,100,280,100); rect(40, 100, 220, 200); rect(200, 220, 40, 80); while (i <= 2) { beginshape(); vertex(x, y); vertex(x+40, y); vertex(x+40, y+40); vertex(x, y+40); endshape(close); i++; x = x + 70; } y = y + 100; x = 60; while (x < 200) { rect(x,y,40,40); x = x + 70; } ( Processing window) CGRA 151 Page 4 of??

5 SPARE PAGE FOR EXTRA ANSWERS Cross out rough working that you do not want marked. Specify the question number for work that you do want marked. Below is an extra copy of the template for Question 1(b), in case you make a mistake. (spare copy of Processing window) CGRA 151 Page 5 of??

6 Question 2. Graphics Algorithms [30 marks] (a) [6 marks] Describe two different ways in which the straight line drawing algorithm can be used or the ideas in the algorithm re-purposed to draw 2D elements other than a straight line. Answer 1: Answer 2: CGRA 151 Page 6 of??

7 (b) [6 marks] In the midpoint line drawing algorithm, we normally define a decision variable as: k(x, y) = ax + by + c. For a straight line lying in the first octant, if a point (x, y) is above the straight line, k(x, y) > 0; if (x, y) is below that line, k(x, y) < 0. Assume that we have already turned on the pixel (x p, y p ), then the point we use to evaluate the decision variable is (x p + 1, y p + 0.5). Explain how the decision variable s value is used to decide which pixel should be turned on next. (c) [4 marks] For each of the possible pixels that could be turned on next, show the calculation that updates the decision variable for the following iteration. CGRA 151 Page 7 of??

8 (d) [6 marks] In Cohen-Sutherland s line clipping algorithm, every line endpoint is assigned a 4 bit region code, as shown in the diagram below. The infinite edges of the window to clip against are x = x L, x = x R, y = y T, y = y B. Explain how the region codes are used to decide whether clipping is needed and, if so, how we choose which infinite edge to clip against. (e) [3 marks] You are given the three line segments P 1 P 2, P 3 P 4 and P 5 P 6 shown in the diagram. For each line, state whether Cohen-Sutherland s algorithm will require it to be clipped against some infinite edge. P 1 P 2 P 3 P 4 P 5 P 6 CGRA 151 Page 8 of??

9 (f) [5 marks] For each line, explain why it needs to be clipped or not, and which infinite edge should be clipped against, if applicable. CGRA 151 Page 9 of??

10 SPARE PAGE FOR EXTRA ANSWERS Cross out rough working that you do not want marked. Specify the question number for work that you do want marked. CGRA 151 Page 10 of??

11 Question 3. Colour, Displays, and Human Vision [30 marks] (a) [6 marks] Pick two of the following three-dimensional colour spaces: Lab, HSL, XYZ. Explain what each of the three dimensions represents. Your first choice of colour space is: [3 marks: 1 mark for each dimension] First dimension: Second dimension: Third dimension: Your second choice of colour space is: [3 marks: 1 mark for each dimension] First dimension: Second dimension: Third dimension: CGRA 151 Page 11 of??

12 (b) [6 marks] Explain why red, green and blue are the three primary colours for television. (c) [4 marks] The world s largest LED display screen is made by Colosseo and is installed in the Zenit Arena football stadium in Russia (see above). It is 30 m 10 m in size, with individual pixels that are mm mm. What is the resolution, in pixels, of the screen? Show your working. CGRA 151 Page 12 of??

13 (d) [4 marks] Use your knowledge of the limitations of human vision to calculate the minimum distance that a human being would have to stand from the screen so that the screen s resolution matches or exceeds the resolving ability of the human eye. The human eye has a maximum resolving power of 1/60 of a degree. Show your working. (e) [4 marks] What difference would a human being notice about the screen if they stood significantly closer than the distance you calculated in the previous part? CGRA 151 Page 13 of??

14 (f) [6 marks] The company that built the screen offers an alternative screen with pixels of size 5 mm 5 mm. This screen costs ten times the price of the one that is installed. Stadium management considered installing this higher-resolution screen. Give two reasons, other than the increased price of the screen itself, why you would advise management not to install the higher resolution screen. Reason 1: Reason 2: CGRA 151 Page 14 of??

15 SPARE PAGE FOR EXTRA ANSWERS Cross out rough working that you do not want marked. Specify the question number for work that you do want marked. CGRA 151 Page 15 of??

16 Question 4. Mathematics for graphics [30 marks] (a) [12 marks] Vector and matrix algebra You are given three vectors, p = 2, q = 3 and r = and two matrics, M 1 = and M 2 = 0 0 2, Assume that θ is the angle between the vector p and q. Evaluate the following expressions. Magnitude p = Dot product p q = Angle between vectors p and q θ = Matrix addition M 1 + M 2 = Matrix multiplication 1 M 1 M 2 = Matrix multiplication 2 M 2 r = CGRA 151 Page 16 of??

17 (b) [3 marks] Assume that we have an 2D image plane parallel to the xy plane at a distance d and that we want to project 3D points onto that 2D plane. Give the equations for x and y in terms of x, y, z and d. (c) [6 marks] You are given a triangle ABC in 3D space, where the xyz-coordinates of A, B and C are (6, 10, 4), (1, 2, 2) and (15, 3, 6) respectively, and the distance from the image plane to the origin is d = 2. Calculate the coordinates for the three vertices and draw the projected triangle on the image plane after perspective projection. Show your calculations. Note: The grid is to help you to plot the vertices on the image plane; you do not need to fill the pixels to represent the triangle. (Image plane) CGRA 151 Page 17 of??

18 (d) [9 marks] You are given the 3D object shown below (a teapot). Its centre is at (1, 0, 3). The teapot s axis, which runs from the teapot centre through the centre of the lid, is (0, 1, 0), which is parallel to the y-axis. Describe the minimum transformation steps needed to rotate the teapot 90 degrees about its axis, and show the transformation matrices in homogeneous form for each step. CGRA 151 Page 18 of??

19 Brief Processing documentation You may detach this page from the question paper. void point( float x, float y ) // draw a point at location (x,y) void line( float x1, float y1, float x2, float y2 ) // draw a line segment from location (x1, y1) to location (x2, y2) void rect( float left, float top, float width, float height ) // draw a rectangle with its top left corner at the indicated position // of size width times height void ellipse( float centerx, float centery, float width, float height ) // draw an ellipse centred at the indicated position // of size width times height void triangle( float x1, float y1, float x2, float y2, float x3, float y3 ) // draw a triangle with vertices at the three points // (x1,y1 ), (x2,y2 ), (x3, y3) void beginshape() // start a shape which comprises a sequence of polygon vertices void vertex( float x, float y ) // specify a vertex in the current shape void endshape( mode ) // end and draw a shape. If the mode is CLOSE then the final point // will be connected to the initial point. If the mode is missing then // the shape will be left open. void bezier( float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4 ) // draw a Bezier cubic curve with the four control points // (x1,y1 ), (x2,y2 ), (x3, y3 ), (x4, y4) void background( float grey ) void stroke( float grey ) void fill( float grey ) // set the colour of the background, stroke or fill to be // a grey value between 0 ( black ) and 255 ( white ) void nostroke() void nofill() // turn off drawing strokes around objects and filling objects, respectively * * * * * * * * * * * * * * * CGRA 151 Page 19 of??