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
5. Introduction Architecture Line Drawing Triangle RasterizationCircle Drawing Ellipses
β’ 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
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
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
β’ Data we have: start point between π₯ π , π¦π and π₯ π , π¦ π
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
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
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. π₯ π , π¦ π to π₯ π , π¦π
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
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
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. β’ The equation of a circle may be
expressed in parametric polar form as
follows:
π₯ = π₯ π + π πππ π
π¦ = π¦π + π π πππ
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
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
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
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
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
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
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
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
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