Module Contact: Dr Stephen Laycock, CMP Copyright of the University of East Anglia Version 1

Transcription

1 UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series UG Examination GRAPHICS 1 CMP-51B Time allowed: 2 hours Answer THREE from FOUR questions (4 marks each) Notes are not permitted in this examination. Do not turn over until you are told to do so by the invigilator. CMP-51B Module Contact: Dr Stephen Laycock, CMP Copyright of the University of East Anglia Version 1

2 Page 2 1. Assume you are writing a 2D game in OpenGL where the user controls a car around an urban environment. The game should be viewed from directly above the car. a) You decide to limit the rendering of the game into a viewport which has a 5 pixel border around the edge as illustrated in the diagram below. 5 pixels Window OpenGL rendered area 5 pixels Write the reshape function you would use to set this up in OpenGL. You can assume the reshape function has two arguments which are the width and height of the window in pixels. Describe any special cases you would need to consider as the user changes the size of the window to ensure the objects are rendered without any distortion. b) Some of the buildings in the urban environment are constructed from concave polygons. Describe, with the aid of a diagram, a strategy for computing if the car is colliding with a concave polygon using the crossing number algorithm. c) Describe all of the steps required in texture mapping a car onto a polygon representing a user s vehicle. (8 marks) d) You wish to include a bridge in your 2D environment. The vehicle should be able to drive under the bridge and over the bridge. Describe an approach to allow for this. (4 marks) e) You decide to incorporate 1 other vehicles moving around the urban environment. Describe an approach, using a regular grid, to determine if any of the vehicles in the environment are colliding with each other. (8 marks) (Total: 4 marks)

3 Page 3 2. a) In the context of fonts, describe what is meant by the terms Ligatures, Kerning and Optical Sizing. (6 marks) b) Describe, with the aid of a diagram, how outline fonts work. c) Describe, with the aid of a diagram, how the Separating Axes Theorem works. d) Describe the purpose of the following OpenGL commands i) glpushmatrix(); ii) glpopmatrix(); iii) glloadidentity(); iv) glclearcolor(gl_color_buffer_bit). e) Given two points, A(3,4) and B(4,5), state the parametric equation of a line starting at B and passing through A. State how you might use this equation to animate an object moving from B to A in an OpenGL program. (4 marks) (Total: 4 marks) TURN OVER

4 Page 4 3. a) Answer the questions below, each covering a selected topic from the module lectures. i) Consider the 3D matrices A,B and C for 2D transformations using homogenous coordinates: 1 A B C.5 1 Explain what each of these three matrices will do to a square shape with sides of length 1.. You can draw figures in a 2D coordinate system to illustrate the effect of each transformation. Note that the B(1,1) and B(2,2) entries are cosine values rounded to three decimals. (9 marks) ii) Explain what a metamerism is in colour formation. (4 marks) iii) For the Sutherland Hodgeman polygon clipping algorithm, state the four possible scenarios when processing vertices in sequence around the perimeter of a polygon. (4 marks) iv) For the Cohen-Sutherland line clipping algorithm, draw a clipping window and label each of the eight adjacent regions and the window itself using a four bit code, clearly specifying which bit corresponds to which location. (8 marks)

5 Page 5 b) Imagine we start with a square of size s at the origin as shown in Figure 1 a). We wish to derive the articulated geometry (some kind of robotic arm) as shown in Figure 1 b). Specify the 2D transformation matrices (in the correct order) to arrive at this geometry by solely using three squares all starting in the origin as shown in Figure 1 a). Do this in three steps, i.e. first for the gantry, then for the first link, then for the second link. Keep in mind that the arm should stay together if the second link was moved to a different position. (15 marks) y y 2s s x 2s 2s x 45º (a) (b) Figure 1. (Total: 4 marks) TURN OVER

6 Page 6 4. a) Consider the Sutherland-Hodgeman polygon clipping algorithm. Using the clipping pipeline and the four scenarios to process vertices around the polygon for each of the clipping edges, clip the two polygons in Figure 2 each separately. Specify per polygon all scenarios applied for each clipping edge until the final clipped polygon is obtained. Specify the resulting vertex array after each clipping edge. Update Figure 2 with new vertices corresponding to those used in the vertex array. (2 marks) v 2 v 3 v 1 v 4 v 1 v 11 v 6 v 5 v 12 v 13 Figure 2.

7 Page 7 b) Figure 3 shows a line clipping region with the line P1-P2. Illustrate the Cohen-Sutherland line clipping algorithm for clipping the line P1-P2, clearly outlining the application of each step in the algorithm by referring to the activated programming code line numbers (see next page for programming code). Use a table with the first column containing the active line number(s) in the algorithm, the second column the variable(s) affected and the third column for comments (e.g. which points have been updated and their new IDs). Update Figure 3 with the clipped line and new points (make sure you use the same point IDs as those referred to in the third column of the table). (2 marks) P 2 P 1 Figure 3. TURN OVER

8 Page 8 1. void ClipLine_Cohen_Sutherland(coord winmin, coord winmax, coord p, coord p1){ 2. unsigned char code,code1; 3. int done = FALSE, draw = FALSE; 4. float m; 5. while(!done){ 6. code = encode(p,winmin,winmax); 7. code1 = encode(p1,winmin,winmax); 8. if(accept(code,code1)){ /* Line is entirely inside clip-window */ 9. done = TRUE; 1. draw = TRUE; 11. else { 12. if(reject(code,code1)) 13. done = TRUE; 14. else { 15. if(inside(code)){ /* Init. Point inside clip-window => swap */ 16. swappts(&p,&p1); 17. swapcodes(&code,&code1); 18. if(p1.x!= p.x){ /* No vertical line */ 19. m=((float)(p1->y-p->y))/ ((float)(p1->x-p->x)); 2. if(code & LEFT_EDGE){ 21. p.y += (winmin.x-p.x)*m; 22. p.x = winmin.x; 23. else if(code & RIGHT_EDGE){ 24. p.y += (winmax.x-p.x)*m; 25. p.x = winmax.x; 26. else if(code & BOTTOM_EDGE){ 27. if(p1.x!= p.x)/*none-vert.line*/ 28. p.x += (winmin.y-p.y)/m; 29. p.y = winmin.y; 3. else if(code & TOP_EDGE){ 31. if(p1.x!= p.x)/*none-vert.line*/ 32. p.x += (winmax.y-p.y)/m; 33. p.y = winmax.y; /* end_while */ 34. if(draw)line_dda_b(p.x,p.y,p1.x,p1.y); (Total: 4 marks) END OF PAPER

9 In general we have been pleased with the answers to the exam questions. Out of the four questions set question 2 and 3 were the most popular and question 1 was the least popular. Question 4, was in general the one which most answered well. Question 2 was also answered well.