The document discusses several common algorithms for computer graphics rendering including Bresenham's line drawing algorithm, the midpoint circle algorithm, and scanline polygon filling. Bresenham's algorithm uses only integer calculations to efficiently draw lines. The midpoint circle algorithm incrementally chooses pixel coordinates to draw circles with eightfold symmetry and without floating point operations. Scanline polygon filling finds the edge intersections on each scanline and fills pixels between interior intersections.

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

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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