1. Computer Graphics 4: Bresenham Line Drawing Algorithm, Circle Drawing & Polygon Filling

14. Bresenham Example (cont…) 17 16 15 14 13 12 11 10 18 29 27 26 25 24 23 22 21 20 28 30 k p k (x k+1 ,y k+1 ) 0 1 2 3 4 5 6 7 8 9

16. Bresenham Exercise (cont…) 17 16 15 14 13 12 11 10 18 29 27 26 25 24 23 22 21 20 28 30 k p k (x k+1 ,y k+1 ) 0 1 2 3 4 5 6 7 8

19. A Simple Circle Drawing Algorithm (cont…)

31. Mid-Point Circle Algorithm Example (cont…) 9 7 6 5 4 3 2 1 0 8 9 7 6 5 4 3 2 1 0 8 10 10 k p k (x k+1 ,y k+1 ) 2x k+1 2y k+1 0 1 2 3 4 5 6

33. Mid-Point Circle Algorithm Example (cont…) k p k (x k+1 ,y k+1 ) 2x k+1 2y k+1 0 1 2 3 4 5 6 7 8 9 10 11 12 9 7 6 5 4 3 2 1 0 8 9 7 6 5 4 3 2 1 0 8 10 10 13 12 11 14 15 13 12 14 11 16 15 16

36. Scan-Line Polygon Fill Algorithm 2 4 6 8 10 Scan Line 0 2 4 6 8 10 12 14 16

38. Scan-Line Polygon Fill Algorithm (cont…)

40. Anti-Aliasing

41. Summary Of Drawing Algorithms

42. Mid-Point Circle Algorithm (cont…) 6 2 3 4 1 5 4 3

43. Mid-Point Circle Algorithm (cont…) M 6 2 3 4 1 5 4 3

44. Mid-Point Circle Algorithm (cont…) M 6 2 3 4 1 5 4 3

45. Blank Grid

46. Blank Grid

47. Blank Grid 9 7 6 5 4 3 2 1 0 8 9 7 6 5 4 3 2 1 0 8 10 10

48. Blank Grid