Module Contact: Dr Rudy Lapeer, CMP Copyright of the University of East Anglia Version 1

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1 UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series UG Examination GRAPHICS 1 CMP-5010B Time allowed: 2 hours Answer THREE questions. Notes are not permitted in this examination Do not turn over until you are told to do so by the invigilator. CMP-5010B Module Contact: Dr Rudy Lapeer, CMP Copyright of the University of East Anglia Version 1

2 -2-1. Assume you are a games programmer creating a 2D car racing game, viewed from above the player s vehicle. Other non-player controlled vehicles should be also in the game environment and these should move around the race track. a) The following function is used whenever the game window is moved or resized. void reshape(int w, int h) { glviewport(0,0,w,h); glmatrixmode(gl_projection); glloadidentity(); gluortho2d(-5.0,5.0,-5.0,5.0); glmatrixmode(gl_modelview); glloadidentity(); i. Describe what the commands glviewport and gluortho2d do in the above function. [4 marks] ii. What problem might occur with the display of the vehicles if the above function is used? State an improvement to overcome the problem. [6 marks] b) You decide to define the track by an inner and outer boundary as shown in Figure 1. Tarmac Track Gravel Grass Figure 1.

3 -3- Describe how you could use the line crossing algorithm to compute if the tyres of the vehicle lie within the tarmac track. [15 marks] c) Assuming we have recorded all of the end points of the dashed lines shown in Figure 1, describe a strategy to enable the non-player vehicles to randomly navigate smoothly around the track at a constant speed. [15 marks] PLEASE TURN OVER

4 2. a) In the context of fonts, describe what is meant by the following terms -4- i. Kerning & Ligatures ii. Fixed Pitch iii. Point Size [12 marks] b) Describe an outline font and detail, with the aid of diagrams, how it can be used in practice. [12 marks] c) Assume you have a line segment defined between two points, A and B in two dimensions, as shown in Figure 2. Detail how you could determine which side of the line a third point, C, lies. Illustrate how your method works using the example shown in Figure 2. B(3,7) A(-1,3) C(4,4) Figure 2. [10 marks] d) Using your answer from part c) describe how you could determine if a 2D point is located inside a convex polygon lying in the same plane. Illustrate your answer with an example. [6 marks]

5 -5-3. a) Below is the programming code for circle drawing using the mid-point algorithm: void Circle_Mid(int x0,int y0,int R){ int x=0, y=r, d=1-r; Circle8Seg(x0,y0,x,y); while(y>x){ if(d<0) d+=2*x+3;/* Select E */ else { /* Select SE */ d+=2*(x-y)+5; y--; x++; Circle8Seg(x0,y0,x,y); i. Draw a figure showing the E SE region, the current point, the candidate midpoints(s) and the circle segment. [6 marks] ii. iii. iv. Define the decision variable d according to the mid-point criterion. [6 marks] Calculate the decision variable increments when the E and SE pixels are chosen respectively. [8 marks] Why is the function Circle8Seg( ) called in the above function Circle_Mid( )? [5 marks] PLEASE TURN OVER

6 -6- b) Imagine we start with a square at the origin as shown in Figure 3(a). We wish to derive the articulated geometry (some kind of robotic arm) as shown in Figure 3(b). Specify the 2D transformation matrices (in the right order) to arrive at this geometry by solely using three squares all starting in the origin as shown in Figure 3(a). Do this in three steps, i.e. first for the gantry, then the first link, then for the second link, making sure that the transformations preserve the articulated linkages. [15 marks] y y 2s y 40º 2.5s Gantry s x 3s x (a) (b) Figure 3.

7 -7-4. a) Consider the scan-line algorithm for the polygon in Figure 4. i. Show the relevant scan lines on an updated figure. Also indicate which points need to be lowered on an edge by drawing a dot below the original point and label this new point with the primed label of the original point. [8 marks] ii. Determine the initial bucket-sorted edge table using linked lists. [12 marks] H G F E A B C D Figure 4. PLEASE TURN OVER

8 -8- b) Figure 5 shows a line clipping region. Illustrate the Cohen-Sutherland clipping algorithm for the drawn line P1-P2, clearly outlining the application of each step in the algorithm by referring to the programming code line numbers (see next page for programming code). Update the figure with the clipped points at each stage and the final clipped line. [20 marks] P 2 P 1 Figure 5.

9 -9-1. void ClipLine_Cohen_Sutherland(coord winmin, coord winmax, coord p0,coord p1){ 2. unsigned char code0,code1; 3. int done = FALSE, draw = FALSE; 4. float m; 5. while(!done){ 6. code0 = encode(p0,winmin,winmax); 7. code1 = encode(p1,winmin,winmax); 8. if(accept(code0,code1)){ /* Line is entirely inside clip-window */ 9. done = TRUE; 10. draw = TRUE; 11. else { /* else 1 */ 12. if(reject(code0,code1)) 13. done = TRUE; 14. else { /* else 2 */ 15. if(inside(code0)){ /* Init. Point inside clip-window => swap */ 16. swappts(&p0,&p1); 17. swapcodes(&code0,&code1); 18. if(p1.x!= p0.x){ /* No vertical line */ 19. m=((float)(p1->y-p0->y))/((float)(p1->x-p0->x)); 20. if(code0 & LEFT_EDGE){ 21. p0.y += (winmin.x-p0.x)*m; 22. p0.x = winmin.x; 23. else if(code0 & RIGHT_EDGE){ 24. p0.y += (winmax.x-p0.x)*m; 25. p0.x = winmax.x; 26. else if(code0 & BOTTOM_EDGE){ 27. if(p1.x!= p0.x)/* None-vert.lines*/ 28. p0.x += (winmin.y-p0.y)/m; 29. p0.y = winmin.y; 30. else if(code0 & TOP_EDGE){ 31. if(p1.x!= p0.x)/* None-vert.lines*/ 32. p0.x += (winmax.y-p0.y)/m; 33. p0.y = winmax.y; /* end else 2 */ /* end else 1 */ /* end_while */ 34. if(draw)line_dda_b(p0.x,p0.y,p1.x,p1.y); END OF PAPER