The document discusses different algorithms for computer graphics rasterization. It covers line drawing algorithms like the straightforward approach, DDA, midpoint, and Bresenham's. It also discusses circle drawing using the parametric polar form equation and triangle rasterization which examines pixels using edge equations and colors them using barycentric coordinates.

2. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

3. o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

4. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

5. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses
• The output of the Interpolation Block is series output , So this block will be slow as it includes four
modules (2 Dividers & 2 FIFOs) .

6. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

7. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

8. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

9. A straightforward line drawing algorithm
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

10. The incremental DDA Algorithm
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses
𝑥𝑖+1 = 𝑥𝑖 +
𝑦𝑖+1 = 𝑦𝑖 + 𝑚

11. The incremental DDA Algorithm (Cont.)
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

12. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

13. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses
• Data we have: start point between 𝑥 𝑎 , 𝑦𝑎 and 𝑥 𝑏 , 𝑦 𝑏

14. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

15. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

16. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

17. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

18. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

19. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

20. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

21. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

22. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

23. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

24. 𝑥 𝑏 , 𝑦 𝑏 to 𝑥 𝑎 , 𝑦𝑎
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

25. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

26. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

27. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

28. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

29. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

30. • The equation of a circle may be
expressed in parametric polar form as
follows:
𝑥 = 𝑥 𝑐 + 𝑟 𝑐𝑜𝑠𝜃
𝑦 = 𝑦𝑐 + 𝑟 𝑠𝑖𝑛𝜃
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

31. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

32. Ellipses
(
𝑥 − 𝑥 𝑐
𝑟1
)2+(
𝑦 − 𝑦𝑐
𝑟2
)2= 1
Or
𝑦2 = 𝑟2
2(1 −
𝑥2
𝑟1
2
)
𝑥 = 𝑥 𝑐 + 𝑟 𝑐𝑜𝑠𝜃
𝑦 = 𝑦𝑐 + 𝑟 𝑠𝑖𝑛𝜃
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

33. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

34. Targets
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

35. Steps
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

36. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

37. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

38. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

39. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

40. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

41. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

42. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

43. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

44. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

45. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

46. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

47. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

48. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

49. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

50. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

51. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

52. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

53. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

54. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

55. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

56. o Architecture of Rasterization ?
o Line Drawing
1) Algorithms
1) A straightforward line drawing algorithm & The incremental DDA Algorithm .
2) The Midpoint Line Drawing Algorithm - Pitteway (1967)
3) The Bresenham Line Drawing Algorithm
4) The Double Step Midpoint Line Drawing Algorithm
2) Some points worth considering
o Circle Drawing .
1) The Symmetry of a Circle
2) A Straightforward Circle Drawing Algorithm
3) Use of parametric polar form equation
o Ellipses .
o Triangle Rasterization:
1) Targets & Steps .
2) Edge walking idea(steps).
3) Edge equations
4) Which pixels will be examined?
5) How pixel is colored ?
6) Barycentric coordinates
7) Coloring triangle
8) Shared edges
Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

57. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses

58. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses