1. Computer Graphics Filled Area Primitives II Lecture 09 Taqdees A
Computer Graphics Filled Area Primitives II Lecture 09 Taqdees A. Siddiqi

2. Filled Area Primitives
There are two basic approaches to area filling on raster systems.
scan-line polygon filling
Boundary-fill and Flood-fill

3. Polygon
A polygon can be defined as a shape that is formed by line segments that are placed end to end, creating a continuous closed path. Polygons can be divided into three basic types:
convex
concave
complex

4. Polygon types
Does a straight line connecting ANY two points that are inside the polygon intersect any edges of the polygon?

5. Convex polygons
If the answer is no then polygon is convex

6. Concave polygons
Otherwise the polygon is concave

7. Complex polygons
Complex polygons are basically concave polygons that may have self-intersecting edges

8. Unfilled polygons
When an unfilled polygon is rendered, only the points on the perimeter of the polygon are drawn.

9. Filled Polygons
When a polygon is filled, the interior of the polygon must be considered. All of the pixels within the boundaries of the polygon must be set to the specified color or pattern.

10. Parity
Parity is a concept used to determine which pixels lie within a polygon, i.e. which pixels should be filled for a given polygon.

11. ODD number of edges
Point is inside the polygon filled area

12. Even number of edges I
Point lies outside the polygon

13. Even number of edges II
Point lies outside the circle

14. Polygon Filling Algorithm
When filling a polygon, you will most likely just have a set of vertices, indicating the x and y Cartesian coordinates of each vertex of the polygon. The following steps should be taken to turn your set of vertices into a filled polygon.

15. 1. Initialize all of the edges

16. For each edge, the following information needs to be kept in a table:
The minimum y value of the two vertices
The maximum y value of the two vertices
The x value associated with the minimum y value
The slope of the edge

17. Cont…
The slope of the edge can be calculated from the formula for a line
y = mx + b

18. where
m = slope
b = y-intercept,
y0 = maximum y value,
y1 = minimum y value,
x0 = maximum x value,
x1 = minimum x value
The formula for the slope is as follows:
m = (y0 - y1) / (x0 - x1).

19. Table: All edges Index Y-min Y-max X-val 1/m 10 16 10 1 16 20 10 1.5 -10 16 10 1 16 20 10
1.5 - - - - - - - - N 10 16 28
Table: All edges

20. 2. Initialize the Global edge Table
Edges with the same minimum y values are sorted on minimum x values as follows:
First edge with non zero slope.
If the slope of an edge is zero, do not add it.
For every other edge, start at index 0 and look for an appropriate position for the edge, in ascending order of minimum y-values

21. 3. Initialize Parity
The initial parity is even since no edges have been crossed yet.

22. 4. Initializing the Scan-Line
The initial scan-line is equal to the lowest y value for all of the global edges.

23. 5. Initializing the Active Edge Table
Index
Y-max
X-val
1/m 16 10 1 20
1.5 - N 28

24. 6. Filling the Polygon
Starting with the initial scan-line, until the active edge table is empty, do the following steps:

25. Step 1
Draw all pixels from the x value of odd to the x value of even parity edge pairs.

26. Step 2
Increase the scan-line by 1.

27. Step 3
Remove any edges from the active edge table for which the maximum y value is equal to the scan line.

28. Step 4
Update the x value for each edge in the active edge table using the formula
x1 = x0 + 1/m
(This is based on the line formula and the fact that the next scan-line equals the old scan-line plus one.)

29. Step 5
Remove any edges from the global edge table for which the minimum y value = the scan-line and place them in the active edge table.

30. Step 6
Reorder the edges in the active edge table according to increasing x value. This is done in case edges have crossed.

31. An Example
(10, 10) 1
(10, 16) 2
(16, 20) 3
(28, 10) 4
(28, 16) 5
(22, 10)

32. Steps involved
We will now walk through the steps of the algorithm to fill in the polygon:

33. 1. Initializing All of the Edges
Index
Y-min
Y-max
X-val
1/m 10 16 1 20
1.5 2 28
-1.2 3 4 22 5
Inf

34. 2. Initializing the Global Edge Table:
Index
Y-min
Y-max
X-val
1/m 10 16 1 22 2 28 3 20
-1.2 4
1.5

35. 3. Initialize Parity
Parity is initially set to Even

36. 4. Initializing the Scan-Line
Since the lowest y value in the global edge table is 10, we can safely choose 10 as our initial scan-line.

37. 5. Initializing the Active Edge Table
Index
Y-max
X-val
1/m 16 10 1 22 2 28 3 20
-1.2 4
1.5

38. 6. Filling the polygon

39. 6. Filling the polygon

40. 6. Filling the polygon

41. 6. Filling the polygon

42. 6. Filling the polygon

43. 6. Filling the polygon

44. 6. Filling the polygon

45. 6. Filling the polygon

46. 6. Filling the polygon

47. 6. Filling the polygon

49. Boundary fill Check the pixel for boundary color
Check the pixel for fill color
Set the pixel in fill color
Run the process for neighbors

50. Boundary fill
Boundary fill is pixel checking and setting method that involves following steps:
Check the width and height of area
Get the current pixel
Apply boundary checking
Set the pixel
Call this function recursively and set all neighboring pixels.

51. Process

52. Algorithm BoundaryFill (x, y, fillColor , boundaryColor)
if ((x < 0) || (x >= width)) then return
if ((y < 0) || (y >= height)) then return
current = GetPixel(x, y)

53. Algorithm if ((current != boundaryColor) && (current != fillColor))
setPixel(fillColor, x, y)
BoundaryFill(x+1,y,fillColor,boundaryColor)
BoundaryFill(x,y+1,fillColor,boundaryColor)
BoundaryFill (x-1,y,fillColor,boundaryColor)
BoundaryFill (x,y-1,fillColor,boundaryColor)

54. How about this? ?

55. Flood Fill
An area fill algorithm that replaces all connected pixels of a selected color with a fill color.

58. Algorithm floodFill(x, y, fillColor, oldColor)
if ((x < 0) || (x >= width)) then return
if ((y < 0) || (y >= height)) then return

59. Algorithm if ( getPixel (x, y) == oldColor) then
setPixel (fillColor, x, y)
floodFill (x+1, y, fillColor, oldColor)
floodFill (x, y+1, fillColor, oldColor)
floodFill (x-1, y, fillColor, oldColor)
floodFill (x, y-1, fillColor, oldColor)

60. Neighborhood

61. 4-connected floodFill4 (x+1, y, fillColor, oldColor)

62. 8-connected floodFill8 (x+1, y, fillColor, oldColor)

63. Recursion Recursive calls to functions… When can it cause problems?
Why?
What can be done to prevent the problem?

64. Computer Graphics Filled Area Primitives II Lecture 09 Taqdees A
Computer Graphics Filled Area Primitives II Lecture 09 Taqdees A. Siddiqi